LMFDB - Embedded newform 17.12.c.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(4,17)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.1462i q^{2} +(485.546 + 485.546i) q^{3} +1600.84 q^{4} +(-8779.09 - 8779.09i) q^{5} +(10267.5 - 10267.5i) q^{6} +(43052.7 - 43052.7i) q^{7} -77159.1i q^{8} +294363. i q^{9} +O(q^{10})$	\(q-21.1462i q^{2} +(485.546 + 485.546i) q^{3} +1600.84 q^{4} +(-8779.09 - 8779.09i) q^{5} +(10267.5 - 10267.5i) q^{6} +(43052.7 - 43052.7i) q^{7} -77159.1i q^{8} +294363. i q^{9} +(-185644. + 185644. i) q^{10} +(96729.2 - 96729.2i) q^{11} +(777281. + 777281. i) q^{12} +1.42463e6 q^{13} +(-910401. - 910401. i) q^{14} -8.52531e6i q^{15} +1.64690e6 q^{16} +(-215312. + 5.85026e6i) q^{17} +6.22466e6 q^{18} -1.08888e7i q^{19} +(-1.40539e7 - 1.40539e7i) q^{20} +4.18081e7 q^{21} +(-2.04546e6 - 2.04546e6i) q^{22} +(-1.21423e7 + 1.21423e7i) q^{23} +(3.74643e7 - 3.74643e7i) q^{24} +1.05317e8i q^{25} -3.01256e7i q^{26} +(-5.69139e7 + 5.69139e7i) q^{27} +(6.89204e7 - 6.89204e7i) q^{28} +(-3.88955e7 - 3.88955e7i) q^{29} -1.80278e8 q^{30} +(7.83572e7 + 7.83572e7i) q^{31} -1.92847e8i q^{32} +9.39330e7 q^{33} +(1.23711e8 + 4.55304e6i) q^{34} -7.55927e8 q^{35} +4.71228e8i q^{36} +(8.70621e7 + 8.70621e7i) q^{37} -2.30258e8 q^{38} +(6.91726e8 + 6.91726e8i) q^{39} +(-6.77387e8 + 6.77387e8i) q^{40} +(-4.97068e8 + 4.97068e8i) q^{41} -8.84083e8i q^{42} -1.02943e9i q^{43} +(1.54848e8 - 1.54848e8i) q^{44} +(2.58424e9 - 2.58424e9i) q^{45} +(2.56764e8 + 2.56764e8i) q^{46} -1.14665e9 q^{47} +(7.99644e8 + 7.99644e8i) q^{48} -1.72974e9i q^{49} +2.22705e9 q^{50} +(-2.94512e9 + 2.73603e9i) q^{51} +2.28061e9 q^{52} +1.62274e9i q^{53} +(1.20351e9 + 1.20351e9i) q^{54} -1.69839e9 q^{55} +(-3.32191e9 - 3.32191e9i) q^{56} +(5.28704e9 - 5.28704e9i) q^{57} +(-8.22492e8 + 8.22492e8i) q^{58} +5.07047e9i q^{59} -1.36476e10i q^{60} +(-7.13957e9 + 7.13957e9i) q^{61} +(1.65696e9 - 1.65696e9i) q^{62} +(1.26731e10 + 1.26731e10i) q^{63} -7.05145e8 q^{64} +(-1.25070e10 - 1.25070e10i) q^{65} -1.98633e9i q^{66} -6.49492e9 q^{67} +(-3.44680e8 + 9.36532e9i) q^{68} -1.17913e10 q^{69} +1.59850e10i q^{70} +(1.95043e10 + 1.95043e10i) q^{71} +2.27128e10 q^{72} +(-1.92989e10 - 1.92989e10i) q^{73} +(1.84103e9 - 1.84103e9i) q^{74} +(-5.11362e10 + 5.11362e10i) q^{75} -1.74313e10i q^{76} -8.32891e9i q^{77} +(1.46274e10 - 1.46274e10i) q^{78} +(4.88110e9 - 4.88110e9i) q^{79} +(-1.44583e10 - 1.44583e10i) q^{80} -3.12312e9 q^{81} +(1.05111e10 + 1.05111e10i) q^{82} +1.92016e9i q^{83} +6.69281e10 q^{84} +(5.32502e10 - 4.94697e10i) q^{85} -2.17686e10 q^{86} -3.77711e10i q^{87} +(-7.46354e9 - 7.46354e9i) q^{88} -9.65282e9 q^{89} +(-5.46469e10 - 5.46469e10i) q^{90} +(6.13344e10 - 6.13344e10i) q^{91} +(-1.94379e10 + 1.94379e10i) q^{92} +7.60921e10i q^{93} +2.42472e10i q^{94} +(-9.55941e10 + 9.55941e10i) q^{95} +(9.36363e10 - 9.36363e10i) q^{96} +(8.73365e10 + 8.73365e10i) q^{97} -3.65775e10 q^{98} +(2.84735e10 + 2.84735e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) $ 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7} + 178138 q^{10} - 24816 q^{11} + 1322202 q^{12} - 1533752 q^{13} - 757692 q^{14} + 22082308 q^{16} + 17346416 q^{17} + 16775420 q^{18} + 11716134 q^{20} + 16504072 q^{21} + 55362010 q^{22} - 70945120 q^{23} - 7042078 q^{24} - 27445824 q^{27} + 339432756 q^{28} + 185239264 q^{29} - 1261021320 q^{30} + 415468304 q^{31} - 1075445880 q^{33} + 969384454 q^{34} - 1094449168 q^{35} - 49028824 q^{37} - 1340995872 q^{38} + 3217138400 q^{39} + 1182717098 q^{40} - 1419194816 q^{41} - 509236610 q^{44} + 1839923056 q^{45} - 3796371488 q^{46} - 8774740352 q^{47} + 4059548014 q^{48} + 4114666548 q^{50} - 9057963232 q^{51} + 18756164724 q^{52} + 25648728424 q^{54} - 17548144256 q^{55} + 966113388 q^{56} + 23148052104 q^{57} + 32800009486 q^{58} + 1217387240 q^{61} - 42857202380 q^{62} - 58090649872 q^{63} - 43481694148 q^{64} - 12772720712 q^{65} + 17181896368 q^{67} - 120669329406 q^{68} + 84389704104 q^{69} + 36350065824 q^{71} - 62012005860 q^{72} + 41295758480 q^{73} + 108372466886 q^{74} + 143581200752 q^{75} + 103160490932 q^{78} - 86305741264 q^{79} - 278909687742 q^{80} - 398139885080 q^{81} + 84221472400 q^{82} + 278009687832 q^{84} - 131899000528 q^{85} + 214354160644 q^{86} + 95628137594 q^{88} - 158760835496 q^{89} + 629605313178 q^{90} + 149211106624 q^{91} + 288480507416 q^{92} - 267919909216 q^{95} - 242746850002 q^{96} - 126853433800 q^{97} - 829249376752 q^{98} + 229465269792 q^{99}+O(q^{100}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7 + 178138 * q^10 - 24816 * q^11 + 1322202 * q^12 - 1533752 * q^13 - 757692 * q^14 + 22082308 * q^16 + 17346416 * q^17 + 16775420 * q^18 + 11716134 * q^20 + 16504072 * q^21 + 55362010 * q^22 - 70945120 * q^23 - 7042078 * q^24 - 27445824 * q^27 + 339432756 * q^28 + 185239264 * q^29 - 1261021320 * q^30 + 415468304 * q^31 - 1075445880 * q^33 + 969384454 * q^34 - 1094449168 * q^35 - 49028824 * q^37 - 1340995872 * q^38 + 3217138400 * q^39 + 1182717098 * q^40 - 1419194816 * q^41 - 509236610 * q^44 + 1839923056 * q^45 - 3796371488 * q^46 - 8774740352 * q^47 + 4059548014 * q^48 + 4114666548 * q^50 - 9057963232 * q^51 + 18756164724 * q^52 + 25648728424 * q^54 - 17548144256 * q^55 + 966113388 * q^56 + 23148052104 * q^57 + 32800009486 * q^58 + 1217387240 * q^61 - 42857202380 * q^62 - 58090649872 * q^63 - 43481694148 * q^64 - 12772720712 * q^65 + 17181896368 * q^67 - 120669329406 * q^68 + 84389704104 * q^69 + 36350065824 * q^71 - 62012005860 * q^72 + 41295758480 * q^73 + 108372466886 * q^74 + 143581200752 * q^75 + 103160490932 * q^78 - 86305741264 * q^79 - 278909687742 * q^80 - 398139885080 * q^81 + 84221472400 * q^82 + 278009687832 * q^84 - 131899000528 * q^85 + 214354160644 * q^86 + 95628137594 * q^88 - 158760835496 * q^89 + 629605313178 * q^90 + 149211106624 * q^91 + 288480507416 * q^92 - 267919909216 * q^95 - 242746850002 * q^96 - 126853433800 * q^97 - 829249376752 * q^98 + 229465269792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	21.1462i		−	0.467269i	−0.972324	−	0.233635i	$-0.924938\pi$
$2$		−	21.1462i		−	0.467269i	0.972324	−	0.233635i	$-0.0750620\pi$
$3$	485.546	+	485.546i	1.15362	+	1.15362i	0.985821	+	0.167802i	$0.0536668\pi$
$3$	485.546	+	485.546i	1.15362	+	1.15362i	0.167802	+	0.985821i	$0.446333\pi$
$4$	1600.84			0.781659
$5$	−8779.09	−	8779.09i	−1.25636	−	1.25636i	−0.952817	−	0.303544i	$-0.901830\pi$
$5$	−8779.09	−	8779.09i	−1.25636	−	1.25636i	−0.303544	−	0.952817i	$-0.598170\pi$
$6$	10267.5	−	10267.5i	0.539052	−	0.539052i
$7$	43052.7	−	43052.7i	0.968191	−	0.968191i	−0.0313183	−	0.999509i	$-0.509971\pi$
$7$	43052.7	−	43052.7i	0.968191	−	0.968191i	0.999509	+	0.0313183i	$0.00997056\pi$
$8$		−	77159.1i		−	0.832515i
$9$			294363.i			1.66169i
$10$	−185644.	+	185644.i	−0.587059	+	0.587059i
$11$	96729.2	−	96729.2i	0.181091	−	0.181091i	−0.610740	−	0.791831i	$-0.709128\pi$
$11$	96729.2	−	96729.2i	0.181091	−	0.181091i	0.791831	+	0.610740i	$0.209128\pi$
$12$	777281.	+	777281.i	0.901740	+	0.901740i
$13$	1.42463e6			1.06418			0.532090	−	0.846688i	$-0.321407\pi$
$13$	1.42463e6			1.06418			0.532090	+	0.846688i	$0.321407\pi$
$14$	−910401.	−	910401.i	−0.452406	−	0.452406i
$15$		−	8.52531e6i		−	2.89873i
$16$	1.64690e6			0.392651
$17$	−215312.	+	5.85026e6i	−0.0367790	+	0.999323i
$17$	−215312.	+	5.85026e6i	−0.0367790	+	0.999323i
$18$	6.22466e6			0.776457
$19$		−	1.08888e7i		−	1.00887i	−0.863449	−	0.504437i	$-0.831700\pi$
$19$		−	1.08888e7i		−	1.00887i	0.863449	−	0.504437i	$-0.168300\pi$
$20$	−1.40539e7	−	1.40539e7i	−0.982047	−	0.982047i
$21$	4.18081e7			2.23385
$22$	−2.04546e6	−	2.04546e6i	−0.0846185	−	0.0846185i
$23$	−1.21423e7	+	1.21423e7i	−0.393368	+	0.393368i	−0.875886	−	0.482518i	$-0.839722\pi$
$23$	−1.21423e7	+	1.21423e7i	−0.393368	+	0.393368i	0.482518	+	0.875886i	$0.339722\pi$
$24$	3.74643e7	−	3.74643e7i	0.960408	−	0.960408i
$25$			1.05317e8i			2.15689i
$26$		−	3.01256e7i		−	0.497259i
$27$	−5.69139e7	+	5.69139e7i	−0.763340	+	0.763340i
$28$	6.89204e7	−	6.89204e7i	0.756796	−	0.756796i
$29$	−3.88955e7	−	3.88955e7i	−0.352136	−	0.352136i	0.508768	−	0.860904i	$-0.330101\pi$
$29$	−3.88955e7	−	3.88955e7i	−0.352136	−	0.352136i	−0.860904	+	0.508768i	$0.830101\pi$
$30$	−1.80278e8			−1.35449
$31$	7.83572e7	+	7.83572e7i	0.491575	+	0.491575i	0.908802	−	0.417227i	$-0.136998\pi$
$31$	7.83572e7	+	7.83572e7i	0.491575	+	0.491575i	−0.417227	+	0.908802i	$0.636998\pi$
$32$		−	1.92847e8i		−	1.01599i
$33$	9.39330e7			0.417822
$34$	1.23711e8	+	4.55304e6i	0.466953	+	0.0171857i
$35$	−7.55927e8			−2.43280
$36$			4.71228e8i			1.29888i
$37$	8.70621e7	+	8.70621e7i	0.206405	+	0.206405i	0.802737	−	0.596333i	$-0.203376\pi$
$37$	8.70621e7	+	8.70621e7i	0.206405	+	0.206405i	−0.596333	+	0.802737i	$0.703376\pi$
$38$	−2.30258e8			−0.471416
$39$	6.91726e8	+	6.91726e8i	1.22766	+	1.22766i
$40$	−6.77387e8	+	6.77387e8i	−1.04594	+	1.04594i
$41$	−4.97068e8	+	4.97068e8i	−0.670046	+	0.670046i	−0.957726	−	0.287681i	$-0.907116\pi$
$41$	−4.97068e8	+	4.97068e8i	−0.670046	+	0.670046i	0.287681	+	0.957726i	$0.407116\pi$
$42$		−	8.84083e8i		−	1.04381i
$43$		−	1.02943e9i		−	1.06788i	−0.845523	−	0.533939i	$-0.820711\pi$
$43$		−	1.02943e9i		−	1.06788i	0.845523	−	0.533939i	$-0.179289\pi$
$44$	1.54848e8	−	1.54848e8i	0.141552	−	0.141552i
$45$	2.58424e9	−	2.58424e9i	2.08768	−	2.08768i
$46$	2.56764e8	+	2.56764e8i	0.183809	+	0.183809i
$47$	−1.14665e9			−0.729274			−0.364637	−	0.931150i	$-0.618807\pi$
$47$	−1.14665e9			−0.729274			−0.364637	+	0.931150i	$0.618807\pi$
$48$	7.99644e8	+	7.99644e8i	0.452971	+	0.452971i
$49$		−	1.72974e9i		−	0.874788i
$50$	2.22705e9			1.00785
$51$	−2.94512e9	+	2.73603e9i	−1.19527	+	1.11041i
$52$	2.28061e9			0.831826
$53$			1.62274e9i			0.533004i	0.963834	+	0.266502i	$0.0858680\pi$
$53$			1.62274e9i			0.533004i	−0.963834	+	0.266502i	$0.914132\pi$
$54$	1.20351e9	+	1.20351e9i	0.356685	+	0.356685i
$55$	−1.69839e9			−0.455033
$56$	−3.32191e9	−	3.32191e9i	−0.806034	−	0.806034i
$57$	5.28704e9	−	5.28704e9i	1.16386	−	1.16386i
$58$	−8.22492e8	+	8.22492e8i	−0.164542	+	0.164542i
$59$			5.07047e9i			0.923342i	0.887051	+	0.461671i	$0.152750\pi$
$59$			5.07047e9i			0.923342i	−0.887051	+	0.461671i	$0.847250\pi$
$60$		−	1.36476e10i		−	2.26582i
$61$	−7.13957e9	+	7.13957e9i	−1.08233	+	1.08233i	−0.0860339	+	0.996292i	$0.527419\pi$
$61$	−7.13957e9	+	7.13957e9i	−1.08233	+	1.08233i	−0.996292	+	0.0860339i	$0.972581\pi$
$62$	1.65696e9	−	1.65696e9i	0.229698	−	0.229698i
$63$	1.26731e10	+	1.26731e10i	1.60883	+	1.60883i
$64$	−7.05145e8			−0.0820897
$65$	−1.25070e10	−	1.25070e10i	−1.33699	−	1.33699i
$66$		−	1.98633e9i		−	0.195236i
$67$	−6.49492e9			−0.587709			−0.293854	−	0.955850i	$-0.594938\pi$
$67$	−6.49492e9			−0.587709			−0.293854	+	0.955850i	$0.594938\pi$
$68$	−3.44680e8	+	9.36532e9i	−0.0287486	+	0.781130i
$69$	−1.17913e10			−0.907596
$70$			1.59850e10i			1.13677i
$71$	1.95043e10	+	1.95043e10i	1.28295	+	1.28295i	0.938980	+	0.343970i	$0.111772\pi$
$71$	1.95043e10	+	1.95043e10i	1.28295	+	1.28295i	0.343970	+	0.938980i	$0.388228\pi$
$72$	2.27128e10			1.38338
$73$	−1.92989e10	−	1.92989e10i	−1.08957	−	1.08957i	−0.995572	−	0.0940015i	$-0.970034\pi$
$73$	−1.92989e10	−	1.92989e10i	−1.08957	−	1.08957i	−0.0940015	−	0.995572i	$-0.529966\pi$
$74$	1.84103e9	−	1.84103e9i	0.0964466	−	0.0964466i
$75$	−5.11362e10	+	5.11362e10i	−2.48823	+	2.48823i
$76$		−	1.74313e10i		−	0.788596i
$77$		−	8.32891e9i		−	0.350662i
$78$	1.46274e10	−	1.46274e10i	0.573649	−	0.573649i
$79$	4.88110e9	−	4.88110e9i	0.178471	−	0.178471i	−0.612218	−	0.790689i	$-0.709722\pi$
$79$	4.88110e9	−	4.88110e9i	0.178471	−	0.178471i	0.790689	+	0.612218i	$0.209722\pi$
$80$	−1.44583e10	−	1.44583e10i	−0.493311	−	0.493311i
$81$	−3.12312e9			−0.0995223
$82$	1.05111e10	+	1.05111e10i	0.313092	+	0.313092i
$83$			1.92016e9i			0.0535066i	0.999642	+	0.0267533i	$0.00851686\pi$
$83$			1.92016e9i			0.0535066i	−0.999642	+	0.0267533i	$0.991483\pi$
$84$	6.69281e10			1.74611
$85$	5.32502e10	−	4.94697e10i	1.30172	−	1.20930i
$86$	−2.17686e10			−0.498987
$87$		−	3.77711e10i		−	0.812464i
$88$	−7.46354e9	−	7.46354e9i	−0.150761	−	0.150761i
$89$	−9.65282e9			−0.183235			−0.0916176	−	0.995794i	$-0.529204\pi$
$89$	−9.65282e9			−0.183235			−0.0916176	+	0.995794i	$0.529204\pi$
$90$	−5.46469e10	−	5.46469e10i	−0.975510	−	0.975510i
$91$	6.13344e10	−	6.13344e10i	1.03033	−	1.03033i
$92$	−1.94379e10	+	1.94379e10i	−0.307480	+	0.307480i
$93$			7.60921e10i			1.13418i
$94$			2.42472e10i			0.340768i
$95$	−9.55941e10	+	9.55941e10i	−1.26751	+	1.26751i
$96$	9.36363e10	−	9.36363e10i	1.17207	−	1.17207i
$97$	8.73365e10	+	8.73365e10i	1.03265	+	1.03265i	0.999449	+	0.0331962i	$0.0105686\pi$
$97$	8.73365e10	+	8.73365e10i	1.03265	+	1.03265i	0.0331962	+	0.999449i	$0.489431\pi$
$98$	−3.65775e10			−0.408762
$99$	2.84735e10	+	2.84735e10i	0.300918	+	0.300918i
$100$			1.68595e11i			1.68595i
$101$	1.51904e11			1.43815			0.719073	−	0.694935i	$-0.244567\pi$
$101$	1.51904e11			1.43815			0.719073	+	0.694935i	$0.244567\pi$
$102$	5.78566e10	+	6.22780e10i	0.518862	+	0.558514i
$103$	−2.04056e10			−0.173438			−0.0867189	−	0.996233i	$-0.527638\pi$
$103$	−2.04056e10			−0.173438			−0.0867189	+	0.996233i	$0.527638\pi$
$104$		−	1.09923e11i		−	0.885946i
$105$	−3.67038e11	−	3.67038e11i	−2.80653	−	2.80653i
$106$	3.43147e10			0.249057
$107$	−9.68605e10	−	9.68605e10i	−0.667630	−	0.667630i	0.289537	−	0.957167i	$-0.406499\pi$
$107$	−9.68605e10	−	9.68605e10i	−0.667630	−	0.667630i	−0.957167	+	0.289537i	$0.906499\pi$
$108$	−9.11100e10	+	9.11100e10i	−0.596672	+	0.596672i
$109$	−5.29116e10	+	5.29116e10i	−0.329386	+	0.329386i	−0.852353	−	0.522967i	$-0.824825\pi$
$109$	−5.29116e10	+	5.29116e10i	−0.329386	+	0.329386i	0.522967	+	0.852353i	$0.324825\pi$
$110$			3.59145e10i			0.212623i
$111$			8.45453e10i			0.476226i
$112$	7.09033e10	−	7.09033e10i	0.380161	−	0.380161i
$113$	−5.10947e10	+	5.10947e10i	−0.260882	+	0.260882i	−0.825412	−	0.564530i	$-0.809057\pi$
$113$	−5.10947e10	+	5.10947e10i	−0.260882	+	0.260882i	0.564530	+	0.825412i	$0.309057\pi$
$114$	−1.11801e11	−	1.11801e11i	−0.543836	−	0.543836i
$115$	2.13197e11			0.988425
$116$	−6.22654e10	−	6.22654e10i	−0.275250	−	0.275250i
$117$			4.19360e11i			1.76834i
$118$	1.07221e11			0.431449
$119$	2.42600e11	+	2.61139e11i	0.931927	+	1.00315i
$120$	−6.57805e11			−2.41324
$121$			2.66599e11i			0.934412i
$122$	1.50975e11	+	1.50975e11i	0.505738	+	0.505738i
$123$	−4.82699e11			−1.54596
$124$	1.25437e11	+	1.25437e11i	0.384244	+	0.384244i
$125$	4.95919e11	−	4.95919e11i	1.45347	−	1.45347i
$126$	2.67989e11	−	2.67989e11i	0.751758	−	0.751758i
$127$			4.50488e11i			1.20994i	0.796249	+	0.604969i	$0.206814\pi$
$127$			4.50488e11i			1.20994i	−0.796249	+	0.604969i	$0.793186\pi$
$128$		−	3.80040e11i		−	0.977630i
$129$	4.99838e11	−	4.99838e11i	1.23193	−	1.23193i
$130$	−2.64476e11	+	2.64476e11i	−0.624737	+	0.624737i
$131$	−2.94458e11	−	2.94458e11i	−0.666854	−	0.666854i	0.290133	−	0.956986i	$-0.406301\pi$
$131$	−2.94458e11	−	2.94458e11i	−0.666854	−	0.666854i	−0.956986	+	0.290133i	$0.906301\pi$
$132$	1.50372e11			0.326595
$133$	−4.68794e11	−	4.68794e11i	−0.976783	−	0.976783i
$134$			1.37343e11i			0.274618i
$135$	9.99305e11			1.91806
$136$	4.51401e11	+	1.66133e10i	0.831952	+	0.0306191i
$137$	7.18652e11			1.27220			0.636101	−	0.771606i	$-0.280546\pi$
$137$	7.18652e11			1.27220			0.636101	+	0.771606i	$0.280546\pi$
$138$			2.49342e11i			0.424092i
$139$	−2.79304e11	−	2.79304e11i	−0.456558	−	0.456558i	0.440966	−	0.897524i	$-0.354636\pi$
$139$	−2.79304e11	−	2.79304e11i	−0.456558	−	0.456558i	−0.897524	+	0.440966i	$0.854636\pi$
$140$	−1.21012e12			−1.90162
$141$	−5.56749e11	−	5.56749e11i	−0.841307	−	0.841307i
$142$	4.12442e11	−	4.12442e11i	0.599484	−	0.599484i
$143$	1.37804e11	−	1.37804e11i	0.192714	−	0.192714i
$144$			4.84786e11i			0.652463i
$145$			6.82934e11i			0.884820i
$146$	−4.08098e11	+	4.08098e11i	−0.509124	+	0.509124i
$147$	8.39870e11	−	8.39870e11i	1.00918	−	1.00918i
$148$	1.39372e11	+	1.39372e11i	0.161338	+	0.161338i
$149$	−3.79935e11			−0.423823			−0.211911	−	0.977289i	$-0.567969\pi$
$149$	−3.79935e11			−0.423823			−0.211911	+	0.977289i	$0.567969\pi$
$150$	1.08134e12	+	1.08134e12i	1.16268	+	1.16268i
$151$		−	6.24393e11i		−	0.647269i	−0.946182	−	0.323634i	$-0.895095\pi$
$151$		−	6.24393e11i		−	0.647269i	0.946182	−	0.323634i	$-0.104905\pi$
$152$	−8.40173e11			−0.839902
$153$	−1.72210e12	−	6.33800e10i	−1.66057	−	0.0611153i
$154$	−1.76125e11			−0.163854
$155$		−	1.37581e12i		−	1.23519i
$156$	1.10734e12	+	1.10734e12i	0.959613	+	0.959613i
$157$	2.24192e12			1.87574			0.937870	−	0.346987i	$-0.112795\pi$
$157$	2.24192e12			1.87574			0.937870	+	0.346987i	$0.112795\pi$
$158$	−1.03217e11	−	1.03217e11i	−0.0833942	−	0.0833942i
$159$	−7.87914e11	+	7.87914e11i	−0.614886	+	0.614886i
$160$	−1.69302e12	+	1.69302e12i	−1.27645	+	1.27645i
$161$			1.04552e12i			0.761711i
$162$			6.60420e10i			0.0465037i
$163$	−1.30858e12	+	1.30858e12i	−0.890774	+	0.890774i	−0.994596	−	0.103822i	$-0.966893\pi$
$163$	−1.30858e12	+	1.30858e12i	−0.890774	+	0.890774i	0.103822	+	0.994596i	$0.466893\pi$
$164$	−7.95725e11	+	7.95725e11i	−0.523748	+	0.523748i
$165$	−8.24647e11	−	8.24647e11i	−0.524936	−	0.524936i
$166$	4.06041e10			0.0250020
$167$	−8.41119e11	−	8.41119e11i	−0.501091	−	0.501091i	0.410686	−	0.911777i	$-0.365289\pi$
$167$	−8.41119e11	−	8.41119e11i	−0.501091	−	0.501091i	−0.911777	+	0.410686i	$0.865289\pi$
$168$		−	3.22588e12i		−	1.85972i
$169$	2.37424e11			0.132479
$170$	−1.04610e12	−	1.12604e12i	−0.565071	−	0.608254i
$171$	3.20527e12			1.67643
$172$		−	1.64796e12i		−	0.834718i
$173$	3.06239e11	+	3.06239e11i	0.150248	+	0.150248i	0.778229	−	0.627981i	$-0.216118\pi$
$173$	3.06239e11	+	3.06239e11i	0.150248	+	0.150248i	−0.627981	+	0.778229i	$0.716118\pi$
$174$	−7.98715e11			−0.379639
$175$	4.53417e12	+	4.53417e12i	2.08828	+	2.08828i
$176$	1.59303e11	−	1.59303e11i	0.0711057	−	0.0711057i
$177$	−2.46195e12	+	2.46195e12i	−1.06519	+	1.06519i
$178$			2.04120e11i			0.0856202i
$179$		−	1.28597e12i		−	0.523044i	−0.965197	−	0.261522i	$-0.915776\pi$
$179$		−	1.28597e12i		−	0.523044i	0.965197	−	0.261522i	$-0.0842244\pi$
$180$	4.13695e12	−	4.13695e12i	1.63186	−	1.63186i
$181$	−1.48697e12	+	1.48697e12i	−0.568946	+	0.568946i	−0.931833	−	0.362887i	$-0.881791\pi$
$181$	−1.48697e12	+	1.48697e12i	−0.568946	+	0.568946i	0.362887	+	0.931833i	$0.381791\pi$
$182$	−1.29699e12	−	1.29699e12i	−0.481442	−	0.481442i
$183$	−6.93319e12			−2.49719
$184$	9.36891e11	+	9.36891e11i	0.327485	+	0.327485i
$185$		−	1.52865e12i		−	0.518638i
$186$	1.60906e12			0.529969
$187$	5.45064e11	+	5.86718e11i	0.174309	+	0.187629i
$188$	−1.83559e12			−0.570044
$189$			4.90060e12i			1.47812i
$190$	2.02145e12	+	2.02145e12i	0.592269	+	0.592269i
$191$	6.54390e12			1.86274			0.931372	−	0.364069i	$-0.118613\pi$
$191$	6.54390e12			1.86274			0.931372	+	0.364069i	$0.118613\pi$
$192$	−3.42381e11	−	3.42381e11i	−0.0947005	−	0.0947005i
$193$	−1.88578e12	+	1.88578e12i	−0.506905	+	0.506905i	−0.913575	−	0.406670i	$-0.866690\pi$
$193$	−1.88578e12	+	1.88578e12i	−0.506905	+	0.506905i	0.406670	+	0.913575i	$0.366690\pi$
$194$	1.84683e12	−	1.84683e12i	0.482523	−	0.482523i
$195$		−	1.21455e13i		−	3.08477i
$196$		−	2.76904e12i		−	0.683786i
$197$	1.04311e12	−	1.04311e12i	0.250475	−	0.250475i	−0.570691	−	0.821165i	$-0.693324\pi$
$197$	1.04311e12	−	1.04311e12i	0.250475	−	0.250475i	0.821165	+	0.570691i	$0.193324\pi$
$198$	6.02107e11	−	6.02107e11i	0.140610	−	0.140610i
$199$	3.42125e11	+	3.42125e11i	0.0777129	+	0.0777129i	0.744895	−	0.667182i	$-0.232500\pi$
$199$	3.42125e11	+	3.42125e11i	0.0777129	+	0.0777129i	−0.667182	+	0.744895i	$0.732500\pi$
$200$	8.12615e12			1.79564
$201$	−3.15358e12	−	3.15358e12i	−0.677994	−	0.677994i
$202$		−	3.21220e12i		−	0.672001i
$203$	−3.34911e12			−0.681870
$204$	−4.71465e12	+	4.37994e12i	−0.934295	+	0.867965i
$205$	8.72761e12			1.68364
$206$			4.31500e11i			0.0810422i
$207$	−3.57426e12	−	3.57426e12i	−0.653656	−	0.653656i
$208$	2.34623e12			0.417851
$209$	−1.05327e12	−	1.05327e12i	−0.182698	−	0.182698i
$210$	−7.76145e12	+	7.76145e12i	−1.31140	+	1.31140i
$211$	1.91713e11	−	1.91713e11i	0.0315571	−	0.0315571i	−0.691152	−	0.722709i	$-0.742897\pi$
$211$	1.91713e11	−	1.91713e11i	0.0315571	−	0.0315571i	0.722709	+	0.691152i	$0.242897\pi$
$212$			2.59774e12i			0.416628i
$213$			1.89405e13i			2.96008i
$214$	−2.04823e12	+	2.04823e12i	−0.311963	+	0.311963i
$215$	−9.03750e12	+	9.03750e12i	−1.34164	+	1.34164i
$216$	4.39143e12	+	4.39143e12i	0.635492	+	0.635492i
$217$	6.74698e12			0.951877
$218$	1.11888e12	+	1.11888e12i	0.153912	+	0.153912i
$219$		−	1.87410e13i		−	2.51391i
$220$	−2.71885e12			−0.355681
$221$	−3.06741e11	+	8.33448e12i	−0.0391395	+	1.06346i
$222$	1.78781e12			0.222526
$223$			4.12815e12i			0.501279i	0.968081	+	0.250639i	$0.0806408\pi$
$223$			4.12815e12i			0.501279i	−0.968081	+	0.250639i	$0.919359\pi$
$224$	−8.30260e12	−	8.30260e12i	−0.983671	−	0.983671i
$225$	−3.10014e13			−3.58408
$226$	1.08046e12	+	1.08046e12i	0.121902	+	0.121902i
$227$	7.17513e12	−	7.17513e12i	0.790110	−	0.790110i	−0.191402	−	0.981512i	$-0.561303\pi$
$227$	7.17513e12	−	7.17513e12i	0.790110	−	0.790110i	0.981512	+	0.191402i	$0.0613035\pi$
$228$	8.46369e12	−	8.46369e12i	0.909742	−	0.909742i
$229$		−	4.83699e12i		−	0.507551i	−0.967263	−	0.253776i	$-0.918327\pi$
$229$		−	4.83699e12i		−	0.507551i	0.967263	−	0.253776i	$-0.0816725\pi$
$230$		−	4.50831e12i		−	0.461861i
$231$	4.04407e12	−	4.04407e12i	0.404532	−	0.404532i
$232$	−3.00114e12	+	3.00114e12i	−0.293158	+	0.293158i
$233$	−4.15753e12	−	4.15753e12i	−0.396623	−	0.396623i	0.480417	−	0.877040i	$-0.340485\pi$
$233$	−4.15753e12	−	4.15753e12i	−0.396623	−	0.396623i	−0.877040	+	0.480417i	$0.840485\pi$
$234$	8.86787e12			0.826290
$235$	1.00665e13	+	1.00665e13i	0.916232	+	0.916232i
$236$			8.11701e12i			0.721739i
$237$	4.74000e12			0.411777
$238$	5.52210e12	−	5.13006e12i	0.468739	−	0.435461i
$239$	−5.38807e12			−0.446936			−0.223468	−	0.974711i	$-0.571738\pi$
$239$	−5.38807e12			−0.446936			−0.223468	+	0.974711i	$0.571738\pi$
$240$		−	1.40403e13i		−	1.13819i
$241$	−6.61706e11	−	6.61706e11i	−0.0524290	−	0.0524290i	0.680406	−	0.732835i	$-0.261803\pi$
$241$	−6.61706e11	−	6.61706e11i	−0.0524290	−	0.0524290i	−0.732835	+	0.680406i	$0.761803\pi$
$242$	5.63755e12			0.436622
$243$	8.56572e12	+	8.56572e12i	0.648529	+	0.648529i
$244$	−1.14293e13	+	1.14293e13i	−0.846010	+	0.846010i
$245$	−1.51856e13	+	1.51856e13i	−1.09905	+	1.09905i
$246$			1.02072e13i			0.722380i
$247$		−	1.55126e13i		−	1.07362i
$248$	6.04597e12	−	6.04597e12i	0.409243	−	0.409243i
$249$	−9.32326e11	+	9.32326e11i	−0.0617265	+	0.0617265i
$250$	−1.04868e13	−	1.04868e13i	−0.679162	−	0.679162i
$251$	−5.20082e12			−0.329508			−0.164754	−	0.986335i	$-0.552683\pi$
$251$	−5.20082e12			−0.329508			−0.164754	+	0.986335i	$0.552683\pi$
$252$	2.02876e13	+	2.02876e13i	1.25756	+	1.25756i
$253$			2.34904e12i			0.142471i
$254$	9.52611e12			0.565367
$255$	4.98753e13	+	1.83560e12i	2.89677	+	0.106612i
$256$	−9.48054e12			−0.538906
$257$		−	2.14552e12i		−	0.119372i	−0.998217	−	0.0596858i	$-0.980990\pi$
$257$		−	2.14552e12i		−	0.119372i	0.998217	−	0.0596858i	$-0.0190099\pi$
$258$	−1.05697e13	−	1.05697e13i	−0.575643	−	0.575643i
$259$	7.49651e12			0.399678
$260$	−2.00217e13	−	2.00217e13i	−1.04507	−	1.04507i
$261$	1.14494e13	−	1.14494e13i	0.585140	−	0.585140i
$262$	−6.22666e12	+	6.22666e12i	−0.311600	+	0.311600i
$263$		−	2.94191e12i		−	0.144169i	−0.997399	−	0.0720847i	$-0.977035\pi$
$263$		−	2.94191e12i		−	0.144169i	0.997399	−	0.0720847i	$-0.0229652\pi$
$264$		−	7.24779e12i		−	0.347843i
$265$	1.42462e13	−	1.42462e13i	0.669646	−	0.669646i
$266$	−9.91321e12	+	9.91321e12i	−0.456421	+	0.456421i
$267$	−4.68689e12	−	4.68689e12i	−0.211384	−	0.211384i
$268$	−1.03973e13			−0.459388
$269$	4.75693e12	+	4.75693e12i	0.205916	+	0.205916i	0.802529	−	0.596613i	$-0.203487\pi$
$269$	4.75693e12	+	4.75693e12i	0.205916	+	0.205916i	−0.596613	+	0.802529i	$0.703487\pi$
$270$		−	2.11315e13i		−	0.896251i
$271$	−2.88756e13			−1.20005			−0.600025	−	0.799981i	$-0.704843\pi$
$271$	−2.88756e13			−1.20005			−0.600025	+	0.799981i	$0.704843\pi$
$272$	−3.54597e11	+	9.63477e12i	−0.0144413	+	0.392385i
$273$	5.95613e13			2.37722
$274$		−	1.51968e13i		−	0.594461i
$275$	1.01872e13	+	1.01872e13i	0.390594	+	0.390594i
$276$	−1.88760e13			−0.709431
$277$	−2.84028e13	−	2.84028e13i	−1.04646	−	1.04646i	−0.998867	−	0.0475939i	$-0.984845\pi$
$277$	−2.84028e13	−	2.84028e13i	−1.04646	−	1.04646i	−0.0475939	−	0.998867i	$-0.515155\pi$
$278$	−5.90622e12	+	5.90622e12i	−0.213336	+	0.213336i
$279$	−2.30655e13	+	2.30655e13i	−0.816845	+	0.816845i
$280$			5.83266e13i			2.02534i
$281$		−	3.97573e13i		−	1.35373i	−0.736107	−	0.676865i	$-0.763338\pi$
$281$		−	3.97573e13i		−	1.35373i	0.736107	−	0.676865i	$-0.236662\pi$
$282$	−1.17731e13	+	1.17731e13i	−0.393117	+	0.393117i
$283$	2.53107e13	−	2.53107e13i	0.828854	−	0.828854i	−0.158504	−	0.987358i	$-0.550667\pi$
$283$	2.53107e13	−	2.53107e13i	0.828854	−	0.828854i	0.987358	+	0.158504i	$0.0506671\pi$
$284$	3.12233e13	+	3.12233e13i	1.00283	+	1.00283i
$285$	−9.28307e13			−2.92446
$286$	−2.91403e12	−	2.91403e12i	−0.0900493	−	0.0900493i
$287$			4.28002e13i			1.29747i
$288$	5.67672e13			1.68826
$289$	−3.41792e13	−	2.51927e12i	−0.997295	−	0.0735082i
$290$	1.44415e13			0.413449
$291$			8.48118e13i			2.38257i
$292$	−3.08944e13	−	3.08944e13i	−0.851675	−	0.851675i
$293$	6.09625e12			0.164927			0.0824634	−	0.996594i	$-0.473721\pi$
$293$	6.09625e12			0.164927			0.0824634	+	0.996594i	$0.473721\pi$
$294$	−1.77601e13	−	1.77601e13i	−0.471557	−	0.471557i
$295$	4.45142e13	−	4.45142e13i	1.16005	−	1.16005i
$296$	6.71763e12	−	6.71763e12i	0.171835	−	0.171835i
$297$			1.10105e13i			0.276469i
$298$			8.03417e12i			0.198039i
$299$	−1.72984e13	+	1.72984e13i	−0.418614	+	0.418614i
$300$	−8.18608e13	+	8.18608e13i	−1.94495	+	1.94495i
$301$	−4.43199e13	−	4.43199e13i	−1.03391	−	1.03391i
$302$	−1.32035e13			−0.302449
$303$	7.37566e13	+	7.37566e13i	1.65908	+	1.65908i
$304$		−	1.79328e13i		−	0.396135i
$305$	1.25358e14			2.71959
$306$	−1.34025e12	+	3.64159e13i	−0.0285573	+	0.775931i
$307$	3.08933e13			0.646552			0.323276	−	0.946305i	$-0.395216\pi$
$307$	3.08933e13			0.646552			0.323276	+	0.946305i	$0.395216\pi$
$308$		−	1.33332e13i		−	0.274098i
$309$	−9.90785e12	−	9.90785e12i	−0.200082	−	0.200082i
$310$	−2.90932e13			−0.577167
$311$	−5.67125e13	−	5.67125e13i	−1.10534	−	1.10534i	−0.993755	−	0.111587i	$-0.964407\pi$
$311$	−5.67125e13	−	5.67125e13i	−1.10534	−	1.10534i	−0.111587	−	0.993755i	$-0.535593\pi$
$312$	5.33729e13	−	5.33729e13i	1.02205	−	1.02205i
$313$	−5.31375e13	+	5.31375e13i	−0.999786	+	0.999786i	−1.00000		0.000213786i	$-0.999932\pi$
$313$	−5.31375e13	+	5.31375e13i	−0.999786	+	0.999786i	0.000213786		1.00000i	$0.499932\pi$
$314$		−	4.74082e13i		−	0.876476i
$315$		−	2.22517e14i		−	4.04255i
$316$	7.81385e12	−	7.81385e12i	0.139504	−	0.139504i
$317$	4.88392e12	−	4.88392e12i	0.0856925	−	0.0856925i	−0.662961	−	0.748654i	$-0.730701\pi$
$317$	4.88392e12	−	4.88392e12i	0.0856925	−	0.0856925i	0.748654	+	0.662961i	$0.230701\pi$
$318$	1.66614e13	+	1.66614e13i	0.287317	+	0.287317i
$319$	−7.52466e12			−0.127538
$320$	6.19053e12	+	6.19053e12i	0.103134	+	0.103134i
$321$		−	9.40605e13i		−	1.54039i
$322$	2.21088e13			0.355924
$323$	6.37025e13	+	2.34450e12i	1.00819	+	0.0371054i
$324$	−4.99960e12			−0.0777925
$325$			1.50038e14i			2.29532i
$326$	2.76714e13	+	2.76714e13i	0.416231	+	0.416231i
$327$	−5.13820e13			−0.759974
$328$	3.83533e13	+	3.83533e13i	0.557823	+	0.557823i
$329$	−4.93662e13	+	4.93662e13i	−0.706077	+	0.706077i
$330$	−1.74381e13	+	1.74381e13i	−0.245287	+	0.245287i
$331$		−	7.55270e13i		−	1.04484i	−0.852690	−	0.522418i	$-0.825030\pi$
$331$		−	7.55270e13i		−	1.04484i	0.852690	−	0.522418i	$-0.174970\pi$
$332$			3.07386e12i			0.0418240i
$333$	−2.56279e13	+	2.56279e13i	−0.342980	+	0.342980i
$334$	−1.77865e13	+	1.77865e13i	−0.234145	+	0.234145i
$335$	5.70195e13	+	5.70195e13i	0.738375	+	0.738375i
$336$	6.88537e13			0.877124
$337$	−8.48203e12	−	8.48203e12i	−0.106301	−	0.106301i	0.651956	−	0.758257i	$-0.273949\pi$
$337$	−8.48203e12	−	8.48203e12i	−0.106301	−	0.106301i	−0.758257	+	0.651956i	$0.773949\pi$
$338$		−	5.02062e12i		−	0.0619035i
$339$	−4.96177e13			−0.601919
$340$	8.52450e13	−	7.91930e13i	1.01750	−	0.945264i
$341$	1.51589e13			0.178040
$342$		−	6.77794e13i		−	0.783347i
$343$	1.06592e13	+	1.06592e13i	0.121229	+	0.121229i
$344$	−7.94302e13			−0.889025
$345$	1.03517e14	+	1.03517e14i	1.14027	+	1.14027i
$346$	6.47580e12	−	6.47580e12i	0.0702061	−	0.0702061i
$347$	1.31572e13	−	1.31572e13i	0.140395	−	0.140395i	−0.633416	−	0.773811i	$-0.718348\pi$
$347$	1.31572e13	−	1.31572e13i	0.140395	−	0.140395i	0.773811	+	0.633416i	$0.218348\pi$
$348$		−	6.04654e13i		−	0.635070i
$349$			1.40427e14i			1.45181i	0.687795	+	0.725905i	$0.258579\pi$
$349$			1.40427e14i			1.45181i	−0.687795	+	0.725905i	$0.741421\pi$
$350$	9.58805e13	−	9.58805e13i	0.975789	−	0.975789i
$351$	−8.10816e13	+	8.10816e13i	−0.812331	+	0.812331i
$352$	−1.86540e13	−	1.86540e13i	−0.183987	−	0.183987i
$353$	−1.35721e14			−1.31792			−0.658958	−	0.752180i	$-0.729003\pi$
$353$	−1.35721e14			−1.31792			−0.658958	+	0.752180i	$0.729003\pi$
$354$	5.20609e13	+	5.20609e13i	0.497730	+	0.497730i
$355$		−	3.42461e14i		−	3.22370i
$356$	−1.54526e13			−0.143228
$357$	−9.00181e12	+	2.44589e14i	−0.0821589	+	2.23234i
$358$	−2.71933e13			−0.244403
$359$		−	1.43058e14i		−	1.26618i	−0.774080	−	0.633088i	$-0.781787\pi$
$359$		−	1.43058e14i		−	1.26618i	0.774080	−	0.633088i	$-0.218213\pi$
$360$	−1.99398e14	−	1.99398e14i	−1.73803	−	1.73803i
$361$	−2.07658e12			−0.0178262
$362$	3.14439e13	+	3.14439e13i	0.265851	+	0.265851i
$363$	−1.29446e14	+	1.29446e14i	−1.07796	+	1.07796i
$364$	9.81864e13	−	9.81864e13i	0.805367	−	0.805367i
$365$			3.38853e14i			2.73780i
$366$			1.46611e14i			1.16686i
$367$	−2.29598e13	+	2.29598e13i	−0.180013	+	0.180013i	−0.791362	−	0.611348i	$-0.790627\pi$
$367$	−2.29598e13	+	2.29598e13i	−0.180013	+	0.180013i	0.611348	+	0.791362i	$0.290627\pi$
$368$	−1.99972e13	+	1.99972e13i	−0.154456	+	0.154456i
$369$	−1.46319e14	−	1.46319e14i	−1.11341	−	1.11341i
$370$	−3.23252e13			−0.242344
$371$	6.98632e13	+	6.98632e13i	0.516050	+	0.516050i
$372$			1.21811e14i			0.886545i
$373$	−9.77394e13			−0.700924			−0.350462	−	0.936577i	$-0.613975\pi$
$373$	−9.77394e13			−0.700924			−0.350462	+	0.936577i	$0.613975\pi$
$374$	1.24069e13	−	1.15260e13i	0.0876734	−	0.0814491i
$375$	4.81584e14			3.35351
$376$			8.84741e13i			0.607132i
$377$	−5.54119e13	−	5.54119e13i	−0.374736	−	0.374736i
$378$	1.03629e14			0.690679
$379$	−1.96656e14	−	1.96656e14i	−1.29179	−	1.29179i	−0.933682	−	0.358104i	$-0.883423\pi$
$379$	−1.96656e14	−	1.96656e14i	−1.29179	−	1.29179i	−0.358104	−	0.933682i	$-0.616577\pi$
$380$	−1.53031e14	+	1.53031e14i	−0.990761	+	0.990761i
$381$	−2.18733e14	+	2.18733e14i	−1.39581	+	1.39581i
$382$		−	1.38379e14i		−	0.870403i
$383$			5.19347e13i			0.322006i	0.986954	+	0.161003i	$0.0514730\pi$
$383$			5.19347e13i			0.322006i	−0.986954	+	0.161003i	$0.948527\pi$
$384$	1.84527e14	−	1.84527e14i	1.12782	−	1.12782i
$385$	−7.31203e13	+	7.31203e13i	−0.440559	+	0.440559i
$386$	3.98771e13	+	3.98771e13i	0.236861	+	0.236861i
$387$	3.03028e14			1.77448
$388$	1.39812e14	+	1.39812e14i	0.807177	+	0.807177i
$389$		−	1.87913e14i		−	1.06963i	−0.844970	−	0.534814i	$-0.820381\pi$
$389$		−	1.87913e14i		−	1.06963i	0.844970	−	0.534814i	$-0.179619\pi$
$390$	−2.56830e14			−1.44142
$391$	−6.84214e13	−	7.36502e13i	−0.378634	−	0.407570i
$392$	−1.33465e14			−0.728274
$393$		−	2.85946e14i		−	1.53860i
$394$	−2.20577e13	−	2.20577e13i	−0.117039	−	0.117039i
$395$	−8.57032e13			−0.448449
$396$	4.55815e13	+	4.55815e13i	0.235215	+	0.235215i
$397$	−1.87470e13	+	1.87470e13i	−0.0954078	+	0.0954078i	−0.753200	−	0.657792i	$-0.771491\pi$
$397$	−1.87470e13	+	1.87470e13i	−0.0954078	+	0.0954078i	0.657792	+	0.753200i	$0.271491\pi$
$398$	7.23465e12	−	7.23465e12i	0.0363129	−	0.0363129i
$399$		−	4.55242e14i		−	2.25368i
$400$			1.73446e14i			0.846904i
$401$	2.85072e14	−	2.85072e14i	1.37297	−	1.37297i	0.516951	−	0.856015i	$-0.327067\pi$
$401$	2.85072e14	−	2.85072e14i	1.37297	−	1.37297i	0.856015	−	0.516951i	$-0.172933\pi$
$402$	−6.66863e13	+	6.66863e13i	−0.316806	+	0.316806i
$403$	1.11630e14	+	1.11630e14i	0.523124	+	0.523124i
$404$	2.43174e14			1.12414
$405$	2.74181e13	+	2.74181e13i	0.125036	+	0.125036i
$406$			7.08210e13i			0.318617i
$407$	1.68429e13			0.0747562
$408$	2.11109e14	+	2.27242e14i	0.924435	+	0.995081i
$409$	−7.07732e13			−0.305767			−0.152884	−	0.988244i	$-0.548856\pi$
$409$	−7.07732e13			−0.305767			−0.152884	+	0.988244i	$0.548856\pi$
$410$		−	1.84556e14i		−	0.786713i
$411$	3.48939e14	+	3.48939e14i	1.46764	+	1.46764i
$412$	−3.26660e13			−0.135569
$413$	2.18298e14	+	2.18298e14i	0.893971	+	0.893971i
$414$	−7.55820e13	+	7.55820e13i	−0.305433	+	0.305433i
$415$	1.68573e13	−	1.68573e13i	0.0672237	−	0.0672237i
$416$		−	2.74737e14i		−	1.08119i
$417$		−	2.71230e14i		−	1.05339i
$418$	−2.22726e13	+	2.22726e13i	−0.0853694	+	0.0853694i
$419$	−2.40841e14	+	2.40841e14i	−0.911073	+	0.911073i	−0.996357	−	0.0852841i	$-0.972820\pi$
$419$	−2.40841e14	+	2.40841e14i	−0.911073	+	0.911073i	0.0852841	+	0.996357i	$0.472820\pi$
$420$	−5.87568e14	−	5.87568e14i	−2.19375	−	2.19375i
$421$	3.14199e14			1.15785			0.578926	−	0.815380i	$-0.303472\pi$
$421$	3.14199e14			1.15785			0.578926	+	0.815380i	$0.303472\pi$
$422$	−4.05399e12	−	4.05399e12i	−0.0147457	−	0.0147457i
$423$		−	3.37530e14i		−	1.21183i
$424$	1.25209e14			0.443734
$425$	−6.16131e14	−	2.26760e13i	−2.15543	−	0.0793282i
$426$	4.00520e14			1.38316
$427$			6.14756e14i			2.09580i
$428$	−1.55058e14	−	1.55058e14i	−0.521859	−	0.521859i
$429$	1.33820e14			0.444638
$430$	1.91109e14	+	1.91109e14i	0.626908	+	0.626908i
$431$	8.33728e13	−	8.33728e13i	0.270022	−	0.270022i	−0.559087	−	0.829109i	$-0.688848\pi$
$431$	8.33728e13	−	8.33728e13i	0.270022	−	0.270022i	0.829109	+	0.559087i	$0.188848\pi$
$432$	−9.37313e13	+	9.37313e13i	−0.299726	+	0.299726i
$433$			1.57685e14i			0.497860i	0.968522	+	0.248930i	$0.0800789\pi$
$433$			1.57685e14i			0.497860i	−0.968522	+	0.248930i	$0.919921\pi$
$434$		−	1.42673e14i		−	0.444783i
$435$	−3.31596e14	+	3.31596e14i	−1.02075	+	1.02075i
$436$	−8.47028e13	+	8.47028e13i	−0.257467	+	0.257467i
$437$	1.32216e14	+	1.32216e14i	0.396859	+	0.396859i
$438$	−3.96301e14			−1.17467
$439$	−1.90761e14	−	1.90761e14i	−0.558385	−	0.558385i	0.370462	−	0.928847i	$-0.379199\pi$
$439$	−1.90761e14	−	1.90761e14i	−0.558385	−	0.558385i	−0.928847	+	0.370462i	$0.879199\pi$
$440$			1.31046e14i			0.378822i
$441$	5.09173e14			1.45363
$442$	1.76243e14	+	6.48641e12i	0.496922	+	0.0182887i
$443$	−2.99514e14			−0.834060			−0.417030	−	0.908893i	$-0.636929\pi$
$443$	−2.99514e14			−0.834060			−0.417030	+	0.908893i	$0.636929\pi$
$444$			1.35343e14i			0.372247i
$445$	8.47430e13	+	8.47430e13i	0.230210	+	0.230210i
$446$	8.72948e13			0.234232
$447$	−1.84476e14	−	1.84476e14i	−0.488932	−	0.488932i
$448$	−3.03584e13	+	3.03584e13i	−0.0794785	+	0.0794785i
$449$	5.79799e13	−	5.79799e13i	0.149942	−	0.149942i	−0.628150	−	0.778092i	$-0.716188\pi$
$449$	5.79799e13	−	5.79799e13i	0.149942	−	0.149942i	0.778092	+	0.628150i	$0.216188\pi$
$450$			6.55562e14i			1.67473i
$451$			9.61620e13i			0.242679i
$452$	−8.17943e13	+	8.17943e13i	−0.203921	+	0.203921i
$453$	3.03171e14	−	3.03171e14i	0.746704	−	0.746704i
$454$	−1.51727e14	−	1.51727e14i	−0.369194	−	0.369194i
$455$	−1.07692e15			−2.58893
$456$	−4.07943e14	−	4.07943e14i	−0.968930	−	0.968930i
$457$		−	4.64323e14i		−	1.08964i	−0.838555	−	0.544818i	$-0.816599\pi$
$457$		−	4.64323e14i		−	1.08964i	0.838555	−	0.544818i	$-0.183401\pi$
$458$	−1.02284e14			−0.237163
$459$	−3.20707e14	−	3.45216e14i	−0.734748	−	0.790898i
$460$	3.41295e14			0.772612
$461$			2.81930e13i			0.0630647i	0.999503	+	0.0315323i	$0.0100387\pi$
$461$			2.81930e13i			0.0630647i	−0.999503	+	0.0315323i	$0.989961\pi$
$462$	−8.55167e13	−	8.55167e13i	−0.189025	−	0.189025i
$463$	2.94502e14			0.643269			0.321634	−	0.946864i	$-0.395768\pi$
$463$	2.94502e14			0.643269			0.321634	+	0.946864i	$0.395768\pi$
$464$	−6.40568e13	−	6.40568e13i	−0.138266	−	0.138266i
$465$	6.68020e14	−	6.68020e14i	1.42494	−	1.42494i
$466$	−8.79160e13	+	8.79160e13i	−0.185330	+	0.185330i
$467$			4.09318e14i			0.852742i	0.904548	+	0.426371i	$0.140208\pi$
$467$			4.09318e14i			0.852742i	−0.904548	+	0.426371i	$0.859792\pi$
$468$			6.71328e14i			1.38224i
$469$	−2.79624e14	+	2.79624e14i	−0.569015	+	0.569015i
$470$	2.12868e14	−	2.12868e14i	0.428127	−	0.428127i
$471$	1.08856e15	+	1.08856e15i	2.16390	+	2.16390i
$472$	3.91233e14			0.768696
$473$	−9.95764e13	−	9.95764e13i	−0.193384	−	0.193384i
$474$		−	1.00233e14i		−	0.192411i
$475$	1.14678e15			2.17603
$476$	3.88363e14	+	4.18042e14i	0.728449	+	0.784118i
$477$	−4.77674e14			−0.885688
$478$			1.13937e14i			0.208839i
$479$	−1.46721e14	−	1.46721e14i	−0.265857	−	0.265857i	0.561572	−	0.827428i	$-0.310197\pi$
$479$	−1.46721e14	−	1.46721e14i	−0.265857	−	0.265857i	−0.827428	+	0.561572i	$0.810197\pi$
$480$	−1.64408e15			−2.94508
$481$	1.24032e14	+	1.24032e14i	0.219652	+	0.219652i
$482$	−1.39926e13	+	1.39926e13i	−0.0244985	+	0.0244985i
$483$	−5.07649e14	+	5.07649e14i	−0.878727	+	0.878727i
$484$			4.26781e14i			0.730392i
$485$		−	1.53347e15i		−	2.59475i
$486$	1.81132e14	−	1.81132e14i	0.303038	−	0.303038i
$487$	2.47255e14	−	2.47255e14i	0.409012	−	0.409012i	−0.472382	−	0.881394i	$-0.656606\pi$
$487$	2.47255e14	−	2.47255e14i	0.409012	−	0.409012i	0.881394	+	0.472382i	$0.156606\pi$
$488$	5.50883e14	+	5.50883e14i	0.901053	+	0.901053i
$489$	−1.27075e15			−2.05523
$490$	3.21117e14	+	3.21117e14i	0.513552	+	0.513552i
$491$			2.82611e14i			0.446931i	0.974712	+	0.223466i	$0.0717371\pi$
$491$			2.82611e14i			0.446931i	−0.974712	+	0.223466i	$0.928263\pi$
$492$	−7.72723e14			−1.20841
$493$	2.35923e14	−	2.19174e14i	0.364849	−	0.338946i
$494$	−3.28033e14			−0.501671
$495$		−	4.99944e14i		−	0.756123i
$496$	1.29046e14	+	1.29046e14i	0.193017	+	0.193017i
$497$	1.67943e15			2.48428
$498$	1.97152e13	+	1.97152e13i	0.0288429	+	0.0288429i
$499$	2.11437e14	−	2.11437e14i	0.305934	−	0.305934i	−0.537396	−	0.843330i	$-0.680592\pi$
$499$	2.11437e14	−	2.11437e14i	0.305934	−	0.305934i	0.843330	+	0.537396i	$0.180592\pi$
$500$	7.93887e14	−	7.93887e14i	1.13612	−	1.13612i
$501$		−	8.16804e14i		−	1.15614i
$502$			1.09978e14i			0.153969i
$503$	3.49507e14	−	3.49507e14i	0.483985	−	0.483985i	−0.422417	−	0.906402i	$-0.638818\pi$
$503$	3.49507e14	−	3.49507e14i	0.483985	−	0.483985i	0.906402	+	0.422417i	$0.138818\pi$
$504$	9.77847e14	−	9.77847e14i	1.33938	−	1.33938i
$505$	−1.33358e15	−	1.33358e15i	−1.80683	−	1.80683i
$506$	4.96732e13			0.0665724
$507$	1.15280e14	+	1.15280e14i	0.152831	+	0.152831i
$508$			7.21159e14i			0.945759i
$509$	8.96075e14			1.16251			0.581255	−	0.813722i	$-0.302562\pi$
$509$	8.96075e14			1.16251			0.581255	+	0.813722i	$0.302562\pi$
$510$	3.88161e13	−	1.05467e15i	0.0498168	−	1.35357i
$511$	−1.66174e15			−2.10983
$512$		−	5.77845e14i		−	0.725816i
$513$	6.19727e14	+	6.19727e14i	0.770113	+	0.770113i
$514$	−4.53697e13			−0.0557787
$515$	1.79142e14	+	1.79142e14i	0.217901	+	0.217901i
$516$	8.00160e14	−	8.00160e14i	0.962949	−	0.962949i
$517$	−1.10914e14	+	1.10914e14i	−0.132065	+	0.132065i
$518$		−	1.58523e14i		−	0.186757i
$519$			2.97387e14i			0.346658i
$520$	−9.65028e14	+	9.65028e14i	−1.11307	+	1.11307i
$521$	−7.01752e14	+	7.01752e14i	−0.800896	+	0.800896i	−0.983236	−	0.182340i	$-0.941633\pi$
$521$	−7.01752e14	+	7.01752e14i	−0.800896	+	0.800896i	0.182340	+	0.983236i	$0.441633\pi$
$522$	−2.42111e14	−	2.42111e14i	−0.273418	−	0.273418i
$523$	1.55822e15			1.74128			0.870641	−	0.491920i	$-0.163705\pi$
$523$	1.55822e15			1.74128			0.870641	+	0.491920i	$0.163705\pi$
$524$	−4.71379e14	−	4.71379e14i	−0.521252	−	0.521252i
$525$			4.40310e15i			4.81817i
$526$	−6.22102e13			−0.0673659
$527$	−4.75281e14	+	4.41539e14i	−0.509322	+	0.473163i
$528$	1.54698e14			0.164058
$529$			6.57937e14i			0.690523i
$530$	−3.01252e14	−	3.01252e14i	−0.312905	−	0.312905i
$531$	−1.49256e15			−1.53431
$532$	−7.50463e14	−	7.50463e14i	−0.763511	−	0.763511i
$533$	−7.08140e14	+	7.08140e14i	−0.713050	+	0.713050i
$534$	−9.91099e13	+	9.91099e13i	−0.0987734	+	0.0987734i
$535$			1.70069e15i			1.67757i
$536$			5.01142e14i			0.489276i
$537$	6.24397e14	−	6.24397e14i	0.603396	−	0.603396i
$538$	1.00591e14	−	1.00591e14i	0.0962181	−	0.0962181i
$539$	−1.67317e14	−	1.67317e14i	−0.158417	−	0.158417i
$540$	1.59973e15			1.49927
$541$	−3.83533e14	−	3.83533e14i	−0.355809	−	0.355809i	0.506456	−	0.862266i	$-0.330955\pi$
$541$	−3.83533e14	−	3.83533e14i	−0.355809	−	0.355809i	−0.862266	+	0.506456i	$0.830955\pi$
$542$			6.10609e14i			0.560747i
$543$	−1.44399e15			−1.31270
$544$	1.12821e15	+	4.15224e13i	1.01530	+	0.0373670i
$545$	9.29031e14			0.827655
$546$		−	1.25950e15i		−	1.11080i
$547$	−5.29597e13	−	5.29597e13i	−0.0462397	−	0.0462397i	0.683609	−	0.729849i	$-0.260409\pi$
$547$	−5.29597e13	−	5.29597e13i	−0.0462397	−	0.0462397i	−0.729849	+	0.683609i	$0.760409\pi$
$548$	1.15045e15			0.994428
$549$	−2.10163e15	−	2.10163e15i	−1.79849	−	1.79849i
$550$	2.15421e14	−	2.15421e14i	0.182513	−	0.182513i
$551$	−4.23527e14	+	4.23527e14i	−0.355261	+	0.355261i
$552$			9.09808e14i			0.755588i
$553$		−	4.20289e14i		−	0.345589i
$554$	−6.00612e14	+	6.00612e14i	−0.488979	+	0.488979i
$555$	7.42231e14	−	7.42231e14i	0.598312	−	0.598312i
$556$	−4.47121e14	−	4.47121e14i	−0.356873	−	0.356873i
$557$	7.72222e14			0.610293			0.305147	−	0.952305i	$-0.401295\pi$
$557$	7.72222e14			0.610293			0.305147	+	0.952305i	$0.401295\pi$
$558$	4.87747e14	+	4.87747e14i	0.381687	+	0.381687i
$559$		−	1.46657e15i		−	1.13642i
$560$	−1.24493e15			−0.955239
$561$	−2.02249e13	+	5.49533e14i	−0.0153671	+	0.417540i
$562$	−8.40716e14			−0.632557
$563$			8.05958e13i			0.0600505i	0.999549	+	0.0300252i	$0.00955877\pi$
$563$			8.05958e13i			0.0600505i	−0.999549	+	0.0300252i	$0.990441\pi$
$564$	−8.91266e14	−	8.91266e14i	−0.657616	−	0.657616i
$565$	8.97130e14			0.655524
$566$	−5.35224e14	−	5.35224e14i	−0.387298	−	0.387298i
$567$	−1.34459e14	+	1.34459e14i	−0.0963566	+	0.0963566i
$568$	1.50494e15	−	1.50494e15i	1.06808	−	1.06808i
$569$		−	2.24839e15i		−	1.58036i	−0.612878	−	0.790178i	$-0.709988\pi$
$569$		−	2.24839e15i		−	1.58036i	0.612878	−	0.790178i	$-0.290012\pi$
$570$			1.96302e15i			1.36651i
$571$	−1.81542e15	+	1.81542e15i	−1.25164	+	1.25164i	−0.296653	+	0.954985i	$0.595870\pi$
$571$	−1.81542e15	+	1.81542e15i	−1.25164	+	1.25164i	−0.954985	+	0.296653i	$0.904130\pi$
$572$	2.20602e14	−	2.20602e14i	0.150637	−	0.150637i
$573$	3.17737e15	+	3.17737e15i	2.14890	+	2.14890i
$574$	9.05062e14			0.606266
$575$	−1.27879e15	−	1.27879e15i	−0.848451	−	0.848451i
$576$		−	2.07569e14i		−	0.136408i
$577$	−2.20500e15			−1.43530			−0.717648	−	0.696406i	$-0.754781\pi$
$577$	−2.20500e15			−1.43530			−0.717648	+	0.696406i	$0.754781\pi$
$578$	−5.32729e13	+	7.22760e14i	−0.0343481	+	0.466005i
$579$	−1.83127e15			−1.16955
$580$			1.09327e15i			0.691628i
$581$	8.26680e13	+	8.26680e13i	0.0518047	+	0.0518047i
$582$	1.79345e15			1.11330
$583$	1.56966e14	+	1.56966e14i	0.0965226	+	0.0965226i
$584$	−1.48908e15	+	1.48908e15i	−0.907086	+	0.907086i
$585$	3.68160e15	−	3.68160e15i	2.22167	−	2.22167i
$586$		−	1.28913e14i		−	0.0770652i
$587$			1.92996e15i			1.14298i	0.820609	+	0.571490i	$0.193635\pi$
$587$			1.92996e15i			1.14298i	−0.820609	+	0.571490i	$0.806365\pi$
$588$	1.34450e15	−	1.34450e15i	0.788831	−	0.788831i
$589$	8.53219e14	−	8.53219e14i	0.495937	−	0.495937i
$590$	−9.41305e14	−	9.41305e14i	−0.542056	−	0.542056i
$591$	1.01295e15			0.577906
$592$	1.43382e14	+	1.43382e14i	0.0810449	+	0.0810449i
$593$			2.32630e15i			1.30276i	0.758750	+	0.651382i	$0.225810\pi$
$593$			2.32630e15i			1.30276i	−0.758750	+	0.651382i	$0.774190\pi$
$594$	2.32830e14			0.129185
$595$	1.62760e14	−	4.42237e15i	0.0894758	−	2.43115i
$596$	−6.08214e14			−0.331285
$597$			3.32235e14i			0.179303i
$598$	3.65795e14	+	3.65795e14i	0.195606	+	0.195606i
$599$	−8.60340e14			−0.455851			−0.227925	−	0.973679i	$-0.573194\pi$
$599$	−8.60340e14			−0.455851			−0.227925	+	0.973679i	$0.573194\pi$
$600$	3.94562e15	+	3.94562e15i	2.07149	+	2.07149i
$601$	−1.64072e15	+	1.64072e15i	−0.853542	+	0.853542i	−0.990567	−	0.137026i	$-0.956246\pi$
$601$	−1.64072e15	+	1.64072e15i	−0.853542	+	0.853542i	0.137026	+	0.990567i	$0.456246\pi$
$602$	−9.37198e14	+	9.37198e14i	−0.483115	+	0.483115i
$603$		−	1.91187e15i		−	0.976590i
$604$		−	9.99552e14i		−	0.505944i
$605$	2.34049e15	−	2.34049e15i	1.17396	−	1.17396i
$606$	1.55967e15	−	1.55967e15i	0.775236	−	0.775236i
$607$	4.40825e14	+	4.40825e14i	0.217134	+	0.217134i	0.807290	−	0.590155i	$-0.200934\pi$
$607$	4.40825e14	+	4.40825e14i	0.217134	+	0.217134i	−0.590155	+	0.807290i	$0.700934\pi$
$608$	−2.09988e15			−1.02500
$609$	−1.62615e15	−	1.62615e15i	−0.786620	−	0.786620i
$610$		−	2.65084e15i		−	1.27078i
$611$	−1.63355e15			−0.776079
$612$	−2.75681e15	−	1.01461e14i	−1.29800	−	0.0477713i
$613$	5.92253e14			0.276360			0.138180	−	0.990407i	$-0.455875\pi$
$613$	5.92253e14			0.276360			0.138180	+	0.990407i	$0.455875\pi$
$614$		−	6.53276e14i		−	0.302114i
$615$	4.23766e15	+	4.23766e15i	1.94228	+	1.94228i
$616$	−6.42651e14			−0.291932
$617$	3.00414e15	+	3.00414e15i	1.35255	+	1.35255i	0.882802	+	0.469745i	$0.155654\pi$
$617$	3.00414e15	+	3.00414e15i	1.35255	+	1.35255i	0.469745	+	0.882802i	$0.344346\pi$
$618$	−2.09513e14	+	2.09513e14i	−0.0934921	+	0.0934921i
$619$	−1.73760e14	+	1.73760e14i	−0.0768511	+	0.0768511i	−0.744487	−	0.667636i	$-0.767306\pi$
$619$	−1.73760e14	+	1.73760e14i	−0.0768511	+	0.0768511i	0.667636	+	0.744487i	$0.267306\pi$
$620$		−	2.20245e15i		−	0.965499i
$621$		−	1.38214e15i		−	0.600547i
$622$	−1.19925e15	+	1.19925e15i	−0.516492	+	0.516492i
$623$	−4.15580e14	+	4.15580e14i	−0.177407	+	0.177407i
$624$	1.13920e15	+	1.13920e15i	0.482042	+	0.482042i
$625$	−3.56502e15			−1.49528
$626$	1.12366e15	+	1.12366e15i	0.467169	+	0.467169i
$627$		−	1.02282e15i		−	0.421530i
$628$	3.58896e15			1.46619
$629$	−5.28081e14	+	4.90590e14i	−0.213856	+	0.198674i
$630$	−4.70539e15			−1.88896
$631$		−	3.34042e15i		−	1.32935i	−0.747131	−	0.664676i	$-0.768569\pi$
$631$		−	3.34042e15i		−	1.32935i	0.747131	−	0.664676i	$-0.231431\pi$
$632$	−3.76621e14	−	3.76621e14i	−0.148580	−	0.148580i
$633$	1.86171e14			0.0728100
$634$	−1.03276e14	−	1.03276e14i	−0.0400415	−	0.0400415i
$635$	3.95488e15	−	3.95488e15i	1.52012	−	1.52012i
$636$	−1.26132e15	+	1.26132e15i	−0.480631	+	0.480631i
$637$		−	2.46425e15i		−	0.930932i
$638$			1.59118e14i			0.0595944i
$639$	−5.74136e15	+	5.74136e15i	−2.13187	+	2.13187i
$640$	−3.33641e15	+	3.33641e15i	−1.22826	+	1.22826i
$641$	2.21361e15	+	2.21361e15i	0.807945	+	0.807945i	0.984323	−	0.176377i	$-0.0564379\pi$
$641$	2.21361e15	+	2.21361e15i	0.807945	+	0.807945i	−0.176377	+	0.984323i	$0.556438\pi$
$642$	−1.98902e15			−0.719775
$643$	−2.09309e15	−	2.09309e15i	−0.750978	−	0.750978i	0.223684	−	0.974662i	$-0.428192\pi$
$643$	−2.09309e15	−	2.09309e15i	−0.750978	−	0.750978i	−0.974662	+	0.223684i	$0.928192\pi$
$644$			1.67371e15i			0.595398i
$645$	−8.77625e15			−3.09550
$646$	4.95773e13	−	1.34707e15i	0.0173382	−	0.471097i
$647$	3.05610e15			1.05973			0.529864	−	0.848082i	$-0.322243\pi$
$647$	3.05610e15			1.05973			0.529864	+	0.848082i	$0.322243\pi$
$648$			2.40977e14i			0.0828538i
$649$	4.90463e14	+	4.90463e14i	0.167209	+	0.167209i
$650$	3.17273e15			1.07253
$651$	3.27597e15	+	3.27597e15i	1.09811	+	1.09811i
$652$	−2.09482e15	+	2.09482e15i	−0.696281	+	0.696281i
$653$	1.32381e15	−	1.32381e15i	0.436317	−	0.436317i	−0.454454	−	0.890770i	$-0.650165\pi$
$653$	1.32381e15	−	1.32381e15i	0.436317	−	0.436317i	0.890770	+	0.454454i	$0.150165\pi$
$654$			1.08653e15i			0.355112i
$655$			5.17014e15i			1.67562i
$656$	−8.18619e14	+	8.18619e14i	−0.263094	+	0.263094i
$657$	5.68088e15	−	5.68088e15i	1.81053	−	1.81053i
$658$	1.04391e15	+	1.04391e15i	0.329928	+	0.329928i
$659$	3.65996e15			1.14711			0.573556	−	0.819166i	$-0.305563\pi$
$659$	3.65996e15			1.14711			0.573556	+	0.819166i	$0.305563\pi$
$660$	−1.32013e15	−	1.32013e15i	−0.410321	−	0.410321i
$661$		−	5.10070e15i		−	1.57225i	−0.618066	−	0.786126i	$-0.712084\pi$
$661$		−	5.10070e15i		−	1.57225i	0.618066	−	0.786126i	$-0.287916\pi$
$662$	−1.59711e15			−0.488220
$663$	−4.19571e15	+	3.89784e15i	−1.27198	+	1.18168i
$664$	1.48158e14			0.0445451
$665$			8.23117e15i			2.45438i
$666$	5.41932e14	+	5.41932e14i	0.160264	+	0.160264i
$667$	9.44564e14			0.277038
$668$	−1.34650e15	−	1.34650e15i	−0.391683	−	0.391683i
$669$	−2.00441e15	+	2.00441e15i	−0.578286	+	0.578286i
$670$	1.20575e15	−	1.20575e15i	0.345020	−	0.345020i
$671$			1.38121e15i			0.392000i
$672$		−	8.06259e15i		−	2.26957i
$673$	1.84550e13	−	1.84550e13i	0.00515265	−	0.00515265i	−0.704526	−	0.709678i	$-0.748840\pi$
$673$	1.84550e13	−	1.84550e13i	0.00515265	−	0.00515265i	0.709678	+	0.704526i	$0.248840\pi$
$674$	−1.79363e14	+	1.79363e14i	−0.0496710	+	0.0496710i
$675$	−5.99399e15	−	5.99399e15i	−1.64644	−	1.64644i
$676$	3.80077e14			0.103554
$677$	8.18990e14	+	8.18990e14i	0.221330	+	0.221330i	0.809059	−	0.587728i	$-0.199978\pi$
$677$	8.18990e14	+	8.18990e14i	0.221330	+	0.221330i	−0.587728	+	0.809059i	$0.699978\pi$
$678$			1.04922e15i			0.281258i
$679$	7.52014e15			1.99960
$680$	−3.81704e15	−	4.10874e15i	−1.00676	−	1.08370i
$681$	6.96771e15			1.82298
$682$		−	3.20552e14i		−	0.0831927i
$683$	−1.05767e15	−	1.05767e15i	−0.272293	−	0.272293i	0.557730	−	0.830023i	$-0.311673\pi$
$683$	−1.05767e15	−	1.05767e15i	−0.272293	−	0.272293i	−0.830023	+	0.557730i	$0.811673\pi$
$684$	5.13113e15			1.31040
$685$	−6.30912e15	−	6.30912e15i	−1.59834	−	1.59834i
$686$	2.25401e14	−	2.25401e14i	0.0566466	−	0.0566466i
$687$	2.34858e15	−	2.34858e15i	0.585523	−	0.585523i
$688$		−	1.69537e15i		−	0.419303i
$689$			2.31181e15i			0.567213i
$690$	2.18899e15	−	2.18899e15i	0.532813	−	0.532813i
$691$	−2.63813e15	+	2.63813e15i	−0.637040	+	0.637040i	−0.949824	−	0.312784i	$-0.898738\pi$
$691$	−2.63813e15	+	2.63813e15i	−0.637040	+	0.637040i	0.312784	+	0.949824i	$0.398738\pi$
$692$	4.90240e14	+	4.90240e14i	0.117442	+	0.117442i
$693$	2.45173e15			0.582692
$694$	−2.78225e14	−	2.78225e14i	−0.0656022	−	0.0656022i
$695$			4.90408e15i			1.14720i
$696$	−2.91438e15			−0.676388
$697$	−2.80095e15	−	3.01500e15i	−0.644949	−	0.694236i
$698$	2.96949e15			0.678386
$699$		−	4.03735e15i		−	0.915107i
$700$	7.25848e15	+	7.25848e15i	1.63232	+	1.63232i
$701$	2.27213e15			0.506973			0.253487	−	0.967339i	$-0.418423\pi$
$701$	2.27213e15			0.506973			0.253487	+	0.967339i	$0.418423\pi$
$702$	1.71457e15	+	1.71457e15i	0.379577	+	0.379577i
$703$	9.48005e14	−	9.48005e14i	0.208236	−	0.208236i
$704$	−6.82081e13	+	6.82081e13i	−0.0148657	+	0.0148657i
$705$			9.77551e15i			2.11397i
$706$			2.86999e15i			0.615822i
$707$	6.53989e15	−	6.53989e15i	1.39240	−	1.39240i
$708$	−3.94118e15	+	3.94118e15i	−0.832614	+	0.832614i
$709$	−4.59781e15	−	4.59781e15i	−0.963822	−	0.963822i	0.0355458	−	0.999368i	$-0.488683\pi$
$709$	−4.59781e15	−	4.59781e15i	−0.963822	−	0.963822i	−0.999368	+	0.0355458i	$0.988683\pi$
$710$	−7.24174e15			−1.50634
$711$	1.43682e15	+	1.43682e15i	0.296564	+	0.296564i
$712$			7.44802e14i			0.152546i
$713$	−1.90288e15			−0.386740
$714$	5.17212e15	+	1.90354e14i	1.04311	+	0.0383903i
$715$	−2.41959e15			−0.484237
$716$		−	2.05863e15i		−	0.408842i
$717$	−2.61616e15	−	2.61616e15i	−0.515595	−	0.515595i
$718$	−3.02514e15			−0.591645
$719$	−2.84142e15	−	2.84142e15i	−0.551475	−	0.551475i	0.375391	−	0.926866i	$-0.377508\pi$
$719$	−2.84142e15	−	2.84142e15i	−0.551475	−	0.551475i	−0.926866	+	0.375391i	$0.877508\pi$
$720$	4.25598e15	−	4.25598e15i	0.819730	−	0.819730i
$721$	−8.78515e14	+	8.78515e14i	−0.167921	+	0.167921i
$722$			4.39118e13i			0.00832965i
$723$		−	6.42578e14i		−	0.120966i
$724$	−2.38041e15	+	2.38041e15i	−0.444722	+	0.444722i
$725$	4.09635e15	−	4.09635e15i	0.759518	−	0.759518i
$726$	2.73729e15	+	2.73729e15i	0.503697	+	0.503697i
$727$	9.85111e15			1.79906			0.899530	−	0.436859i	$-0.143909\pi$
$727$	9.85111e15			1.79906			0.899530	+	0.436859i	$0.143909\pi$
$728$	−4.73250e15	−	4.73250e15i	−0.857765	−	0.857765i
$729$			8.87135e15i			1.59584i
$730$	7.16546e15			1.27929
$731$	6.02246e15	+	2.21650e14i	1.06716	+	0.0392755i
$732$	−1.10989e16			−1.95195
$733$		−	8.73109e14i		−	0.152404i	−0.997092	−	0.0762021i	$-0.975721\pi$
$733$		−	8.73109e14i		−	0.152404i	0.997092	−	0.0762021i	$-0.0242794\pi$
$734$	4.85513e14	+	4.85513e14i	0.0841148	+	0.0841148i
$735$	−1.47466e16			−2.53578
$736$	2.34162e15	+	2.34162e15i	0.399657	+	0.399657i
$737$	−6.28249e14	+	6.28249e14i	−0.106429	+	0.106429i
$738$	−3.09408e15	+	3.09408e15i	−0.520262	+	0.520262i
$739$			6.17849e14i			0.103119i	0.998670	+	0.0515594i	$0.0164191\pi$
$739$			6.17849e14i			0.103119i	−0.998670	+	0.0515594i	$0.983581\pi$
$740$		−	2.44712e15i		−	0.405398i
$741$	7.53209e15	−	7.53209e15i	1.23856	−	1.23856i
$742$	1.47734e15	−	1.47734e15i	0.241134	−	0.241134i
$743$	−8.23840e15	−	8.23840e15i	−1.33476	−	1.33476i	−0.901052	−	0.433711i	$-0.857204\pi$
$743$	−8.23840e15	−	8.23840e15i	−1.33476	−	1.33476i	−0.433711	−	0.901052i	$-0.642796\pi$
$744$	5.87120e15			0.944225
$745$	3.33548e15	+	3.33548e15i	0.532475	+	0.532475i
$746$			2.06682e15i			0.327520i
$747$	−5.65224e14			−0.0889114
$748$	8.72560e14	+	9.39241e14i	0.136250	+	0.146662i
$749$	−8.34021e15			−1.29279
$750$		−	1.01837e16i		−	1.56699i
$751$	−6.97778e15	−	6.97778e15i	−1.06585	−	1.06585i	−0.997673	−	0.0681808i	$-0.978281\pi$
$751$	−6.97778e15	−	6.97778e15i	−1.06585	−	1.06585i	−0.0681808	−	0.997673i	$-0.521719\pi$
$752$	−1.88841e15			−0.286350
$753$	−2.52524e15	−	2.52524e15i	−0.380128	−	0.380128i
$754$	−1.17175e15	+	1.17175e15i	−0.175103	+	0.175103i
$755$	−5.48160e15	+	5.48160e15i	−0.813203	+	0.813203i
$756$			7.84506e15i			1.15538i
$757$			1.04196e16i			1.52344i	0.647908	+	0.761719i	$0.275644\pi$
$757$			1.04196e16i			1.52344i	−0.647908	+	0.761719i	$0.724356\pi$
$758$	−4.15852e15	+	4.15852e15i	−0.603612	+	0.603612i
$759$	−1.14057e15	+	1.14057e15i	−0.164358	+	0.164358i
$760$	7.37595e15	+	7.37595e15i	1.05522	+	1.05522i
$761$	−1.13029e16			−1.60537			−0.802687	−	0.596401i	$-0.796597\pi$
$761$	−1.13029e16			−1.60537			−0.802687	+	0.596401i	$0.796597\pi$
$762$	4.62537e15	+	4.62537e15i	0.652220	+	0.652220i
$763$			4.55597e15i			0.637817i
$764$	1.04757e16			1.45603
$765$	1.45621e16	+	1.56749e16i	2.00949	+	2.16305i
$766$	1.09822e15			0.150464
$767$			7.22357e15i			0.982602i
$768$	−4.60324e15	−	4.60324e15i	−0.621695	−	0.621695i
$769$	−7.44696e14			−0.0998583			−0.0499291	−	0.998753i	$-0.515900\pi$
$769$	−7.44696e14			−0.0998583			−0.0499291	+	0.998753i	$0.515900\pi$
$770$	1.54622e15	+	1.54622e15i	0.205860	+	0.205860i
$771$	1.04175e15	−	1.04175e15i	0.137710	−	0.137710i
$772$	−3.01883e15	+	3.01883e15i	−0.396227	+	0.396227i
$773$		−	6.46506e15i		−	0.842529i	−0.906938	−	0.421265i	$-0.861586\pi$
$773$		−	6.46506e15i		−	0.842529i	0.906938	−	0.421265i	$-0.138414\pi$
$774$		−	6.40788e15i		−	0.829162i
$775$	−8.25233e15	+	8.25233e15i	−1.06027	+	1.06027i
$776$	6.73880e15	−	6.73880e15i	0.859692	−	0.859692i
$777$	3.63990e15	+	3.63990e15i	0.461078	+	0.461078i
$778$	−3.97364e15			−0.499805
$779$	5.41249e15	+	5.41249e15i	0.675992	+	0.675992i
$780$		−	1.94429e16i		−	2.41124i
$781$	3.77328e15			0.464663
$782$	−1.55742e15	+	1.44685e15i	−0.190445	+	0.176924i
$783$	4.42739e15			0.537599
$784$		−	2.84871e15i		−	0.343486i
$785$	−1.96821e16	−	1.96821e16i	−2.35661	−	2.35661i
$786$	−6.04666e15			−0.718938
$787$	2.09004e14	+	2.09004e14i	0.0246771	+	0.0246771i	0.719338	−	0.694661i	$-0.244445\pi$
$787$	2.09004e14	+	2.09004e14i	0.0246771	+	0.0246771i	−0.694661	+	0.719338i	$0.744445\pi$
$788$	1.66984e15	−	1.66984e15i	0.195786	−	0.195786i
$789$	1.42843e15	−	1.42843e15i	0.166317	−	0.166317i
$790$			1.81230e15i			0.209546i
$791$			4.39953e15i			0.505167i
$792$	2.19699e15	−	2.19699e15i	0.250519	−	0.250519i
$793$	−1.01713e16	+	1.01713e16i	−1.15179	+	1.15179i
$794$	3.96428e14	+	3.96428e14i	0.0445811	+	0.0445811i
$795$	1.38343e16			1.54504
$796$	5.47687e14	+	5.47687e14i	0.0607450	+	0.0607450i
$797$			6.91355e15i			0.761519i	0.924674	+	0.380759i	$0.124337\pi$
$797$			6.91355e15i			0.761519i	−0.924674	+	0.380759i	$0.875663\pi$
$798$	−9.62664e15			−1.05307
$799$	2.46887e14	−	6.70817e15i	0.0268220	−	0.728781i
$800$	2.03101e16			2.19137
$801$		−	2.84143e15i		−	0.304480i
$802$	−6.02818e15	−	6.02818e15i	−0.641545	−	0.641545i
$803$	−3.73353e15			−0.394625
$804$	−5.04838e15	−	5.04838e15i	−0.529961	−	0.529961i
$805$	9.17872e15	−	9.17872e15i	0.956984	−	0.956984i
$806$	2.36056e15	−	2.36056e15i	0.244440	−	0.244440i
$807$			4.61942e15i			0.475098i
$808$		−	1.17208e16i		−	1.19728i
$809$	−2.93783e15	+	2.93783e15i	−0.298064	+	0.298064i	−0.840255	−	0.542191i	$-0.817595\pi$
$809$	−2.93783e15	+	2.93783e15i	−0.298064	+	0.298064i	0.542191	+	0.840255i	$0.317595\pi$
$810$	5.79789e14	−	5.79789e14i	0.0584255	−	0.0584255i
$811$	6.46301e15	+	6.46301e15i	0.646874	+	0.646874i	0.952236	−	0.305362i	$-0.0987774\pi$
$811$	6.46301e15	+	6.46301e15i	0.646874	+	0.646874i	−0.305362	+	0.952236i	$0.598777\pi$
$812$	−5.36139e15			−0.532990
$813$	−1.40204e16	−	1.40204e16i	−1.38441	−	1.38441i
$814$		−	3.56163e14i		−	0.0349313i
$815$	2.29762e16			2.23827
$816$	−4.85030e15	+	4.50595e15i	−0.469324	+	0.436004i
$817$	−1.12093e16			−1.07736
$818$			1.49658e15i			0.142876i
$819$	1.80546e16	+	1.80546e16i	1.71209	+	1.71209i
$820$	1.39715e16			1.31603
$821$	−9.15989e14	−	9.15989e14i	−0.0857043	−	0.0857043i	0.662955	−	0.748659i	$-0.269302\pi$
$821$	−9.15989e14	−	9.15989e14i	−0.0857043	−	0.0857043i	−0.748659	+	0.662955i	$0.769302\pi$
$822$	7.37873e15	−	7.37873e15i	0.685783	−	0.685783i
$823$	8.31290e15	−	8.31290e15i	0.767456	−	0.767456i	−0.210202	−	0.977658i	$-0.567412\pi$
$823$	8.31290e15	−	8.31290e15i	0.767456	−	0.767456i	0.977658	+	0.210202i	$0.0674122\pi$
$824$			1.57447e15i			0.144390i
$825$			9.89273e15i			0.901196i
$826$	4.61616e15	−	4.61616e15i	0.417725	−	0.417725i
$827$	1.30835e15	−	1.30835e15i	0.117610	−	0.117610i	−0.645852	−	0.763462i	$-0.723498\pi$
$827$	1.30835e15	−	1.30835e15i	0.117610	−	0.117610i	0.763462	+	0.645852i	$0.223498\pi$
$828$	−5.72181e15	−	5.72181e15i	−0.510936	−	0.510936i
$829$	−4.32426e15			−0.383585			−0.191793	−	0.981435i	$-0.561430\pi$
$829$	−4.32426e15			−0.383585			−0.191793	+	0.981435i	$0.561430\pi$
$830$	−3.56467e14	−	3.56467e14i	−0.0314116	−	0.0314116i
$831$		−	2.75818e16i		−	2.41444i
$832$	−1.00457e15			−0.0873582
$833$	1.01194e16	+	3.72435e14i	0.874196	+	0.0321738i
$834$	−5.73549e15			−0.492218
$835$			1.47685e16i			1.25910i
$836$	−1.68611e15	−	1.68611e15i	−0.142808	−	0.142808i
$837$	−8.91924e15			−0.750477
$838$	5.09287e15	+	5.09287e15i	0.425716	+	0.425716i
$839$	−1.05229e16	+	1.05229e16i	−0.873862	+	0.873862i	−0.992891	−	0.119029i	$-0.962022\pi$
$839$	−1.05229e16	+	1.05229e16i	−0.873862	+	0.873862i	0.119029	+	0.992891i	$0.462022\pi$
$840$	−2.83203e16	+	2.83203e16i	−2.33648	+	2.33648i
$841$		−	9.17479e15i		−	0.752001i
$842$		−	6.64411e15i		−	0.541029i
$843$	1.93040e16	−	1.93040e16i	1.56169	−	1.56169i
$844$	3.06901e14	−	3.06901e14i	0.0246669	−	0.0246669i
$845$	−2.08437e15	−	2.08437e15i	−0.166442	−	0.166442i
$846$	−7.13748e15			−0.566250
$847$	1.14778e16	+	1.14778e16i	0.904689	+	0.904689i
$848$			2.67248e15i			0.209285i
$849$	2.45790e16			1.91237
$850$	−4.79511e14	+	1.30288e16i	−0.0370676	+	1.00717i
$851$	−2.11427e15			−0.162386
$852$			3.03207e16i			2.31378i
$853$	1.04097e16	+	1.04097e16i	0.789254	+	0.789254i	0.981372	−	0.192118i	$-0.0615355\pi$
$853$	1.04097e16	+	1.04097e16i	0.789254	+	0.789254i	−0.192118	+	0.981372i	$0.561536\pi$
$854$	1.29997e16			0.979302
$855$	−2.81394e16	−	2.81394e16i	−2.10621	−	2.10621i
$856$	−7.47366e15	+	7.47366e15i	−0.555812	+	0.555812i
$857$	−1.68810e16	+	1.68810e16i	−1.24740	+	1.24740i	−0.290530	+	0.956866i	$0.593832\pi$
$857$	−1.68810e16	+	1.68810e16i	−1.24740	+	1.24740i	−0.956866	+	0.290530i	$0.906168\pi$
$858$		−	2.82979e15i		−	0.207766i
$859$		−	1.95697e16i		−	1.42765i	−0.700325	−	0.713824i	$-0.746962\pi$
$859$		−	1.95697e16i		−	1.42765i	0.700325	−	0.713824i	$-0.253038\pi$
$860$	−1.44676e16	+	1.44676e16i	−1.04871	+	1.04871i
$861$	−2.07815e16	+	2.07815e16i	−1.49678	+	1.49678i
$862$	−1.76302e15	−	1.76302e15i	−0.126173	−	0.126173i
$863$	5.63278e15			0.400556			0.200278	−	0.979739i	$-0.435815\pi$
$863$	5.63278e15			0.400556			0.200278	+	0.979739i	$0.435815\pi$
$864$	1.09757e16	+	1.09757e16i	0.775544	+	0.775544i
$865$		−	5.37701e15i		−	0.377531i
$866$	3.33444e15			0.232635
$867$	−1.53724e16	−	1.78188e16i	−1.06570	−	1.23530i
$868$	1.08008e16			0.744044
$869$		−	9.44290e14i		−	0.0646393i
$870$	7.01200e15	+	7.01200e15i	0.476964	+	0.476964i
$871$	−9.25289e15			−0.625428
$872$	4.08261e15	+	4.08261e15i	0.274219	+	0.274219i
$873$	−2.57086e16	+	2.57086e16i	−1.71594	+	1.71594i
$874$	2.79586e15	−	2.79586e15i	0.185440	−	0.185440i
$875$		−	4.27013e16i		−	2.81447i
$876$		−	3.00013e16i		−	1.96502i
$877$	1.68292e16	−	1.68292e16i	1.09539	−	1.09539i	0.100442	−	0.994943i	$-0.467974\pi$
$877$	1.68292e16	−	1.68292e16i	1.09539	−	1.09539i	0.994943	−	0.100442i	$-0.0320257\pi$
$878$	−4.03386e15	+	4.03386e15i	−0.260916	+	0.260916i
$879$	2.96001e15	+	2.96001e15i	0.190263	+	0.190263i
$880$	−2.79707e15			−0.178669
$881$	−7.00944e15	−	7.00944e15i	−0.444955	−	0.444955i	0.448718	−	0.893673i	$-0.351881\pi$
$881$	−7.00944e15	−	7.00944e15i	−0.444955	−	0.444955i	−0.893673	+	0.448718i	$0.851881\pi$
$882$		−	1.07671e16i		−	0.679235i
$883$	−1.46646e16			−0.919362			−0.459681	−	0.888084i	$-0.652036\pi$
$883$	−1.46646e16			−0.919362			−0.459681	+	0.888084i	$0.652036\pi$
$884$	−4.91043e14	+	1.33422e16i	−0.0305937	+	0.831263i
$885$	4.32274e16			2.67652
$886$			6.33359e15i			0.389731i
$887$	−1.22097e16	−	1.22097e16i	−0.746662	−	0.746662i	0.227189	−	0.973851i	$-0.427047\pi$
$887$	−1.22097e16	−	1.22097e16i	−0.746662	−	0.746662i	−0.973851	+	0.227189i	$0.927047\pi$
$888$	6.52344e15			0.396465
$889$	1.93947e16	+	1.93947e16i	1.17145	+	1.17145i
$890$	1.79199e15	−	1.79199e15i	0.107570	−	0.107570i
$891$	−3.02097e14	+	3.02097e14i	−0.0180226	+	0.0180226i
$892$			6.60851e15i			0.391829i
$893$			1.24856e16i			0.735746i
$894$	−3.90096e15	+	3.90096e15i	−0.228463	+	0.228463i
$895$	−1.12896e16	+	1.12896e16i	−0.657133	+	0.657133i
$896$	−1.63618e16	−	1.63618e16i	−0.946533	−	0.946533i
$897$	−1.67983e16			−0.965846
$898$	−1.22605e15	−	1.22605e15i	−0.0700632	−	0.0700632i
$899$		−	6.09548e15i		−	0.346202i
$900$	−4.96282e16			−2.80153
$901$	−9.49343e15	−	3.49395e14i	−0.532644	−	0.0196034i
$902$	2.03346e15			0.113397
$903$		−	4.30387e16i		−	2.38549i
$904$	3.94242e15	+	3.94242e15i	0.217188	+	0.217188i
$905$	2.61086e16			1.42960
$906$	−6.41092e15	−	6.41092e15i	−0.348912	−	0.348912i
$907$	2.10354e16	−	2.10354e16i	1.13792	−	1.13792i	0.149097	−	0.988823i	$-0.452363\pi$
$907$	2.10354e16	−	2.10354e16i	1.13792	−	1.13792i	0.988823	−	0.149097i	$-0.0476365\pi$
$908$	1.14862e16	−	1.14862e16i	0.617596	−	0.617596i
$909$			4.47151e16i			2.38975i
$910$			2.27728e16i			1.20973i
$911$	−1.84265e16	+	1.84265e16i	−0.972953	+	0.972953i	−0.999644	−	0.0266906i	$-0.991503\pi$
$911$	−1.84265e16	+	1.84265e16i	−0.972953	+	0.972953i	0.0266906	+	0.999644i	$0.491503\pi$
$912$	8.70720e15	−	8.70720e15i	0.456990	−	0.456990i
$913$	1.85736e14	+	1.85736e14i	0.00968960	+	0.00968960i
$914$	−9.81867e15			−0.509153
$915$	6.08671e16	+	6.08671e16i	3.13738	+	3.13738i
$916$		−	7.74324e15i		−	0.396732i
$917$	−2.53544e16			−1.29128
$918$	−7.30000e15	+	6.78173e15i	−0.369562	+	0.343325i
$919$	3.90997e16			1.96761			0.983804	−	0.179247i	$-0.0573660\pi$
$919$	3.90997e16			1.96761			0.983804	+	0.179247i	$0.0573660\pi$
$920$		−	1.64501e16i		−	0.822879i
$921$	1.50001e16	+	1.50001e16i	0.745877	+	0.745877i
$922$	5.96175e14			0.0294682
$923$	2.77865e16	+	2.77865e16i	1.36529	+	1.36529i
$924$	6.47390e15	−	6.47390e15i	0.316206	−	0.316206i
$925$	−9.16910e15	+	9.16910e15i	−0.445192	+	0.445192i
$926$		−	6.22759e15i		−	0.300580i
$927$		−	6.00665e15i		−	0.288200i
$928$	−7.50089e15	+	7.50089e15i	−0.357766	+	0.357766i
$929$	−1.70237e16	+	1.70237e16i	−0.807174	+	0.807174i	−0.984205	−	0.177031i	$-0.943351\pi$
$929$	−1.70237e16	+	1.70237e16i	−0.807174	+	0.807174i	0.177031	+	0.984205i	$0.443351\pi$
$930$	−1.41261e16	−	1.41261e16i	−0.665833	−	0.665833i
$931$	−1.88349e16			−0.882551
$932$	−6.65554e15	−	6.65554e15i	−0.310024	−	0.310024i
$933$		−	5.50731e16i		−	2.55029i
$934$	8.65552e15			0.398460
$935$	3.65684e14	−	9.93602e15i	0.0167356	−	0.454725i
$936$	3.23574e16			1.47217
$937$		−	7.82849e15i		−	0.354087i	−0.984203	−	0.177044i	$-0.943347\pi$
$937$		−	7.82849e15i		−	0.354087i	0.984203	−	0.177044i	$-0.0566533\pi$
$938$	5.91298e15	+	5.91298e15i	0.265883	+	0.265883i
$939$	−5.16014e16			−2.30675
$940$	1.61148e16	+	1.61148e16i	0.716181	+	0.716181i
$941$	−2.77828e15	+	2.77828e15i	−0.122753	+	0.122753i	−0.765815	−	0.643061i	$-0.777664\pi$
$941$	−2.77828e15	+	2.77828e15i	−0.122753	+	0.122753i	0.643061	+	0.765815i	$0.277664\pi$
$942$	2.30189e16	−	2.30189e16i	1.01112	−	1.01112i
$943$		−	1.20711e16i		−	0.527149i
$944$			8.35054e15i			0.362551i
$945$	4.30228e16	−	4.30228e16i	1.85705	−	1.85705i
$946$	−2.10566e15	+	2.10566e15i	−0.0903623	+	0.0903623i
$947$	2.26173e16	+	2.26173e16i	0.964973	+	0.964973i	0.999407	−	0.0344343i	$-0.0109629\pi$
$947$	2.26173e16	+	2.26173e16i	0.964973	+	0.964973i	−0.0344343	+	0.999407i	$0.510963\pi$
$948$	7.58797e15			0.321869
$949$	−2.74939e16	−	2.74939e16i	−1.15950	−	1.15950i
$950$		−	2.42500e16i		−	1.01679i
$951$	4.74274e15			0.197714
$952$	2.01493e16	−	1.87188e16i	0.835133	−	0.775843i
$953$	−2.38695e16			−0.983633			−0.491816	−	0.870699i	$-0.663667\pi$
$953$	−2.38695e16			−0.983633			−0.491816	+	0.870699i	$0.663667\pi$
$954$			1.01010e16i			0.413855i
$955$	−5.74495e16	−	5.74495e16i	−2.34028	−	2.34028i
$956$	−8.62543e15			−0.349351
$957$	−3.65357e15	−	3.65357e15i	−0.147130	−	0.147130i
$958$	−3.10259e15	+	3.10259e15i	−0.124227	+	0.124227i
$959$	3.09399e16	−	3.09399e16i	1.23173	−	1.23173i
$960$			6.01158e15i			0.237956i
$961$		−	1.31288e16i		−	0.516708i
$962$	2.62280e15	−	2.62280e15i	0.102637	−	0.102637i
$963$	2.85122e16	−	2.85122e16i	1.10939	−	1.10939i
$964$	−1.05928e15	−	1.05928e15i	−0.0409816	−	0.0409816i
$965$	3.31109e16			1.27371
$966$	1.07348e16	+	1.07348e16i	0.410602	+	0.410602i
$967$			4.18511e16i			1.59170i	0.605495	+	0.795849i	$0.292975\pi$
$967$			4.18511e16i			1.59170i	−0.605495	+	0.795849i	$0.707025\pi$
$968$	2.05705e16			0.777912
$969$	2.97922e16	+	3.20689e16i	1.12027	+	1.20588i
$970$	−3.24271e16			−1.21245
$971$			2.97278e16i			1.10524i	0.833433	+	0.552621i	$0.186372\pi$
$971$			2.97278e16i			1.10524i	−0.833433	+	0.552621i	$0.813628\pi$
$972$	1.37123e16	+	1.37123e16i	0.506928	+	0.506928i
$973$	−2.40496e16			−0.884071
$974$	−5.22851e15	−	5.22851e15i	−0.191119	−	0.191119i
$975$	−7.28504e16	+	7.28504e16i	−2.64793	+	2.64793i
$976$	−1.17581e16	+	1.17581e16i	−0.424976	+	0.424976i
$977$			1.00159e16i			0.359971i	0.983669	+	0.179986i	$0.0576051\pi$
$977$			1.00159e16i			0.359971i	−0.983669	+	0.179986i	$0.942395\pi$
$978$			2.68715e16i			0.960347i
$979$	−9.33710e14	+	9.33710e14i	−0.0331823	+	0.0331823i
$980$	−2.43096e16	+	2.43096e16i	−0.859083	+	0.859083i
$981$	−1.55752e16	−	1.55752e16i	−0.547337	−	0.547337i
$982$	5.97615e15			0.208837
$983$	3.80245e16	+	3.80245e16i	1.32135	+	1.32135i	0.912681	+	0.408673i	$0.134008\pi$
$983$	3.80245e16	+	3.80245e16i	1.32135	+	1.32135i	0.408673	+	0.912681i	$0.365992\pi$
$984$			3.72446e16i			1.28703i
$985$	−1.83150e16			−0.629374
$986$	−4.63470e15	−	4.98888e15i	−0.158379	−	0.170483i
$987$	−4.79391e16			−1.62909
$988$		−	2.48332e16i		−	0.839208i
$989$	1.24997e16	+	1.24997e16i	0.420070	+	0.420070i
$990$	−1.05719e16			−0.353313
$991$	−5.60251e15	−	5.60251e15i	−0.186199	−	0.186199i	0.607852	−	0.794051i	$-0.292032\pi$
$991$	−5.60251e15	−	5.60251e15i	−0.186199	−	0.186199i	−0.794051	+	0.607852i	$0.792032\pi$
$992$	1.51110e16	−	1.51110e16i	0.499434	−	0.499434i
$993$	3.66718e16	−	3.66718e16i	1.20535	−	1.20535i
$994$		−	3.55135e16i		−	1.16083i
$995$		−	6.00710e15i		−	0.195271i
$996$	−1.49250e15	+	1.49250e15i	−0.0482491	+	0.0482491i
$997$	−4.14242e16	+	4.14242e16i	−1.33178	+	1.33178i	−0.427994	+	0.903782i	$0.640779\pi$
$997$	−4.14242e16	+	4.14242e16i	−1.33178	+	1.33178i	−0.903782	+	0.427994i	$0.859221\pi$
$998$	−4.47108e15	−	4.47108e15i	−0.142953	−	0.142953i
$999$	−9.91009e15			−0.315114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.7	yes	32
17.4	even	4	inner	17.12.c.a.4.10	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.10	✓	32	17.4	even	4	inner
17.12.c.a.13.7	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-21.1462i q^{2} +(485.546 + 485.546i) q^{3} +1600.84 q^{4} +(-8779.09 - 8779.09i) q^{5} +(10267.5 - 10267.5i) q^{6} +(43052.7 - 43052.7i) q^{7} -77159.1i q^{8} +294363. i q^{9} +O(q^{10})\)	\(q-21.1462i q^{2} +(485.546 + 485.546i) q^{3} +1600.84 q^{4} +(-8779.09 - 8779.09i) q^{5} +(10267.5 - 10267.5i) q^{6} +(43052.7 - 43052.7i) q^{7} -77159.1i q^{8} +294363. i q^{9} +(-185644. + 185644. i) q^{10} +(96729.2 - 96729.2i) q^{11} +(777281. + 777281. i) q^{12} +1.42463e6 q^{13} +(-910401. - 910401. i) q^{14} -8.52531e6i q^{15} +1.64690e6 q^{16} +(-215312. + 5.85026e6i) q^{17} +6.22466e6 q^{18} -1.08888e7i q^{19} +(-1.40539e7 - 1.40539e7i) q^{20} +4.18081e7 q^{21} +(-2.04546e6 - 2.04546e6i) q^{22} +(-1.21423e7 + 1.21423e7i) q^{23} +(3.74643e7 - 3.74643e7i) q^{24} +1.05317e8i q^{25} -3.01256e7i q^{26} +(-5.69139e7 + 5.69139e7i) q^{27} +(6.89204e7 - 6.89204e7i) q^{28} +(-3.88955e7 - 3.88955e7i) q^{29} -1.80278e8 q^{30} +(7.83572e7 + 7.83572e7i) q^{31} -1.92847e8i q^{32} +9.39330e7 q^{33} +(1.23711e8 + 4.55304e6i) q^{34} -7.55927e8 q^{35} +4.71228e8i q^{36} +(8.70621e7 + 8.70621e7i) q^{37} -2.30258e8 q^{38} +(6.91726e8 + 6.91726e8i) q^{39} +(-6.77387e8 + 6.77387e8i) q^{40} +(-4.97068e8 + 4.97068e8i) q^{41} -8.84083e8i q^{42} -1.02943e9i q^{43} +(1.54848e8 - 1.54848e8i) q^{44} +(2.58424e9 - 2.58424e9i) q^{45} +(2.56764e8 + 2.56764e8i) q^{46} -1.14665e9 q^{47} +(7.99644e8 + 7.99644e8i) q^{48} -1.72974e9i q^{49} +2.22705e9 q^{50} +(-2.94512e9 + 2.73603e9i) q^{51} +2.28061e9 q^{52} +1.62274e9i q^{53} +(1.20351e9 + 1.20351e9i) q^{54} -1.69839e9 q^{55} +(-3.32191e9 - 3.32191e9i) q^{56} +(5.28704e9 - 5.28704e9i) q^{57} +(-8.22492e8 + 8.22492e8i) q^{58} +5.07047e9i q^{59} -1.36476e10i q^{60} +(-7.13957e9 + 7.13957e9i) q^{61} +(1.65696e9 - 1.65696e9i) q^{62} +(1.26731e10 + 1.26731e10i) q^{63} -7.05145e8 q^{64} +(-1.25070e10 - 1.25070e10i) q^{65} -1.98633e9i q^{66} -6.49492e9 q^{67} +(-3.44680e8 + 9.36532e9i) q^{68} -1.17913e10 q^{69} +1.59850e10i q^{70} +(1.95043e10 + 1.95043e10i) q^{71} +2.27128e10 q^{72} +(-1.92989e10 - 1.92989e10i) q^{73} +(1.84103e9 - 1.84103e9i) q^{74} +(-5.11362e10 + 5.11362e10i) q^{75} -1.74313e10i q^{76} -8.32891e9i q^{77} +(1.46274e10 - 1.46274e10i) q^{78} +(4.88110e9 - 4.88110e9i) q^{79} +(-1.44583e10 - 1.44583e10i) q^{80} -3.12312e9 q^{81} +(1.05111e10 + 1.05111e10i) q^{82} +1.92016e9i q^{83} +6.69281e10 q^{84} +(5.32502e10 - 4.94697e10i) q^{85} -2.17686e10 q^{86} -3.77711e10i q^{87} +(-7.46354e9 - 7.46354e9i) q^{88} -9.65282e9 q^{89} +(-5.46469e10 - 5.46469e10i) q^{90} +(6.13344e10 - 6.13344e10i) q^{91} +(-1.94379e10 + 1.94379e10i) q^{92} +7.60921e10i q^{93} +2.42472e10i q^{94} +(-9.55941e10 + 9.55941e10i) q^{95} +(9.36363e10 - 9.36363e10i) q^{96} +(8.73365e10 + 8.73365e10i) q^{97} -3.65775e10 q^{98} +(2.84735e10 + 2.84735e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7} + 178138 q^{10} - 24816 q^{11} + 1322202 q^{12} - 1533752 q^{13} - 757692 q^{14} + 22082308 q^{16} + 17346416 q^{17} + 16775420 q^{18} + 11716134 q^{20} + 16504072 q^{21} + 55362010 q^{22} - 70945120 q^{23} - 7042078 q^{24} - 27445824 q^{27} + 339432756 q^{28} + 185239264 q^{29} - 1261021320 q^{30} + 415468304 q^{31} - 1075445880 q^{33} + 969384454 q^{34} - 1094449168 q^{35} - 49028824 q^{37} - 1340995872 q^{38} + 3217138400 q^{39} + 1182717098 q^{40} - 1419194816 q^{41} - 509236610 q^{44} + 1839923056 q^{45} - 3796371488 q^{46} - 8774740352 q^{47} + 4059548014 q^{48} + 4114666548 q^{50} - 9057963232 q^{51} + 18756164724 q^{52} + 25648728424 q^{54} - 17548144256 q^{55} + 966113388 q^{56} + 23148052104 q^{57} + 32800009486 q^{58} + 1217387240 q^{61} - 42857202380 q^{62} - 58090649872 q^{63} - 43481694148 q^{64} - 12772720712 q^{65} + 17181896368 q^{67} - 120669329406 q^{68} + 84389704104 q^{69} + 36350065824 q^{71} - 62012005860 q^{72} + 41295758480 q^{73} + 108372466886 q^{74} + 143581200752 q^{75} + 103160490932 q^{78} - 86305741264 q^{79} - 278909687742 q^{80} - 398139885080 q^{81} + 84221472400 q^{82} + 278009687832 q^{84} - 131899000528 q^{85} + 214354160644 q^{86} + 95628137594 q^{88} - 158760835496 q^{89} + 629605313178 q^{90} + 149211106624 q^{91} + 288480507416 q^{92} - 267919909216 q^{95} - 242746850002 q^{96} - 126853433800 q^{97} - 829249376752 q^{98} + 229465269792 q^{99}+O(q^{100}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7 + 178138 * q^10 - 24816 * q^11 + 1322202 * q^12 - 1533752 * q^13 - 757692 * q^14 + 22082308 * q^16 + 17346416 * q^17 + 16775420 * q^18 + 11716134 * q^20 + 16504072 * q^21 + 55362010 * q^22 - 70945120 * q^23 - 7042078 * q^24 - 27445824 * q^27 + 339432756 * q^28 + 185239264 * q^29 - 1261021320 * q^30 + 415468304 * q^31 - 1075445880 * q^33 + 969384454 * q^34 - 1094449168 * q^35 - 49028824 * q^37 - 1340995872 * q^38 + 3217138400 * q^39 + 1182717098 * q^40 - 1419194816 * q^41 - 509236610 * q^44 + 1839923056 * q^45 - 3796371488 * q^46 - 8774740352 * q^47 + 4059548014 * q^48 + 4114666548 * q^50 - 9057963232 * q^51 + 18756164724 * q^52 + 25648728424 * q^54 - 17548144256 * q^55 + 966113388 * q^56 + 23148052104 * q^57 + 32800009486 * q^58 + 1217387240 * q^61 - 42857202380 * q^62 - 58090649872 * q^63 - 43481694148 * q^64 - 12772720712 * q^65 + 17181896368 * q^67 - 120669329406 * q^68 + 84389704104 * q^69 + 36350065824 * q^71 - 62012005860 * q^72 + 41295758480 * q^73 + 108372466886 * q^74 + 143581200752 * q^75 + 103160490932 * q^78 - 86305741264 * q^79 - 278909687742 * q^80 - 398139885080 * q^81 + 84221472400 * q^82 + 278009687832 * q^84 - 131899000528 * q^85 + 214354160644 * q^86 + 95628137594 * q^88 - 158760835496 * q^89 + 629605313178 * q^90 + 149211106624 * q^91 + 288480507416 * q^92 - 267919909216 * q^95 - 242746850002 * q^96 - 126853433800 * q^97 - 829249376752 * q^98 + 229465269792 * q^99

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